Symmetric polynomials and identities for nLie dialgebras
Speaker: Askar Dzhumadil'daev (KazakhBritish Technical University)
Time: September 21, 2024 14:1015:10
Venue: 吉林大学正新楼209
Abstract: Polynomial identities for nLie dialgebras constructed by symmetric polynomials are studied. Constructions are depend from transposed Poisson structures.
Bio: Askar Dzhumadil'daev is a professor of KazakhBritish Technical University, full member of the Kazakhstan National Academy of Science. His research interests concern cohomologies and deformations of Lie algebras, Ncommutators of vector fields, identities of nonassociative algebras and operads theory.
Derivations on Operator Algebras and Quantum Dynamics
Speaker: Shavkat Ayupov (V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences)
Time: September 21, 2024 8:309:30
Venue: 吉林大学正新楼209
Abstract: This talk presents a full resolution of the problem stated by Ayupov in 2000, and partly restated in 2014 by Kadison and Liu, concerning derivations on algebras of measurable operators aﬃliated with von Neumann algebras. First we give preliminaries from the theory of operator algebras, noncommutative integration theory and show the physical background of automorphisms and derivations on operator algebras. The second part of the talk explains a background of the AyupovKadisonLiu Problem and its connection with general derivation theory in operator algebras starting with fundamental results due to Kaplanski, Kadison, Sakai and others. We shall cite and brieﬂy explain major results concerning derivations on algebras of unbounded operators and list results concerning some special cases of the problem. Finally, the main result yielding the full resolution will be stated.
Bio: Shavkat Ayupov is the Director of V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences. His field of scientific interest include Theory of Operator Algebras and Quantum Probability, Structure theory of Nonassociative algebras (Jordan, Lie, Leibniz, etc.). He is the authors of several monograph devoted to Real and Jordan structures on Operator Algebras, also to the structure theory of Leibniz algebras. Sh. Ayupov is a Member of Uzbekistan Academy of Sciences (since 1995), Fellow of TWAS (The World Academy of Sciences) (since 2003), Senior Associate of ICTP (International Centre for Theoretical Physics) (2008 – 2013), Guest Professor of Sichuan University (Chengdu, China) (20152021). He is the Managing Editor of Uzbek Mathematical Journal and editor of “Advances in Operator Theory”. In 2017, he was awarded the State Prize of the first degree in the field of Science and Technology of the Republic of Uzbekistan.
Previous lectures and talks:
Novel gauge theories and induced mathematical structures
Speaker: Thomas Strobl (University of Lyon)
Venue: 吉林大学数学楼第五研讨室
Abstract: The interaction of mathematics with physics often proved to be very fruitful. In this mini course we focus on the construction of novel type of gauge theories inspired by ideas coming from physics and the mathematical structures that come within this procedure. In this way one is led to novel differential geometric and/or algebraic structures of interest in their own right.
Schedule:
Bio: Thomas Strobl is a professor in the mathematics department at the University of Lyon. His work as a mathematical physicist is mainly concerned with geometric and algebraic aspects of sigma models and gauge theories. In 1993, during his PhD thesis and together with P. Schaller, he discovered the Poisson Sigma Model; it was used later by M. Kontsevich to obtain his famous quantization formula. In 2015 he and A. Kotov introduced a generalisation of YangMills gauge theories to the Lie algebroid setting. In total, in his career he authored more than 60 scientific articles.
Killing metrized exact commutative algebras
Speaker: Daniel Fox (Universidad Politécnica de Madrid)
Time: September 05, 2024 20:0022:00
Venue: ZOOM ID：904 645 6677, Password：2024
Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456
Abstract: A commutative algebra is exact if the traces of its multiplication endormophisms vanish and it is Killing metrized if its Killingtype traceform is invariant. Such an algebra is neither unital nor associative. Depending on one's background the class of Killing metrized exact commutative algebras may appear either absurdly special or so overbroad as to be hopeless to study. The extensive list of examples includes deunitalizations of étale associative algebras, deunitalizations of semisimple Jordan algebras, tensor products of semisimple Lie algebras, Griess algebras of certain vertex operator algebras, and certain algebras associated with combinatorial structures such as Steiner triple systems. I will motivate studying Killing metrized exact commutative algebras and explain some constructions based on an analogy between curvature of a connection and the associator of an algebra that can be used to organize their study. These will be used to classify algebras over general fields in dimensions at most four and to identify classes of Killing metrized exact commutative algebras susceptible to further study.
Bio: Daniel Fox is a professor of mathematics at the Universidad Politécnica de Madrid in Spain.
Variations on locality
Speaker: Sylvie Paycha (University of Potsdam)
Time: August 24, 2024 11:0013:00
Venue: 吉林大学数学楼第5研讨室
Abstract: The principle of locality in quantum field theory states that an object is influenced directly only by its immediate surroundings. We introduce locality relations, defined as symmetric binary relations, which capture essential features of locality. Correspondingly we define locality morphisms, namely maps that factorise on products of pairs in the graph of such locality relations. This factorisation is a key property in the context of renormalisation, which served as a motivation for us to introduce the notation of locality in the first place. I will show its efficiency when counting lattice points inside a cone. This apriori infinite cardinal can naturally be renormalised by implementing are gularisation in several variables. There locality plays an essential role in avoiding "fake" finite contributions. It enables a "minimal subtraction scheme" in several variables which singles out a relevant finite part from the a priori infinite cardinal. This is based on joint work with Li Guo and Bin Zhang.
Bio: Sylvie Paycha is a professor at the mathematics department of the University of Potsdam in Germany since 2011 after holding a professorship at the University ClermontAuvergne in France. She received her PhD at the Ruhr University in Bochum. She works in mathematical physics using tools borrowed from pseudodifferential analysis, geometry and number theory.
Separable Volterra operators and generalized Reynolds algebras
Speaker: Li Guo (Rutgers UniversityNewark)
Time: August 23, 2024 11:0013:00
Venue: 吉林大学数学楼第6研讨室
Abstract: The Reynolds operator originated from the wellknown work of Reynolds on fluid mechanics in the late 19th century. The classical example of a Reynolds operator is given by a specific Volterra integral operator, first studied by Reynolds and Rota. In this study, we explore the rich algebraic structures from other Volterra integral operators, when the kernel of the operator is separable. The operator satisfies a generalized Reynolds identity, called the Ddifferential Reynolds identity. To construct the corresponding free objects, we develop a completion for topological operated algebras and define a completion of the shuffle product. The construction provides an algebraic framework to define and study Volterra integral equations with separable kernels. This is a joint work with Richard Gustavson and Yunnan Li.
Bio: 郭锂，美国罗格斯大学纽瓦克分校教授。他的数论工作为怀尔斯证明费马大定理的文章所引用，并将重整化这一物理方法应用于数学研究。他近年来推动RotaBaxter代数及相关数学和数学物理的研究，应邀为美国数学会在“What Is”栏目中介绍RotaBaxter代数，并出版这个领域的第一部专著。研究涉及结合代数，李代数，Hopf代数，operad，数论，组合，计算数学，量子场论和可积系统等广泛领域。
Scurvature of homogeneous Finsler spaces
Speaker: Shaoqiang Deng (南开大学数学科学学院)
Time: August 16, 2024 14:0016:00
Venue: 吉林大学数学楼第5研讨室
Abstract: In this talk, we present our recent results on Scurvature of homogeneous Finsler spaces. We show that a geodesic orbit Finler spaces has vanishing Scurvature. Then we construct some examples of reversible nonBerwald spaces with vanishing Scurvature. We present an explicit formula of the Scurvature of homogeneous Randers spaces, and give a complete classification of homogeneous Randers spaces with positive flag curvature and vanishing Scurvature.
Bio: 邓少强，南开大学数学科学学院教授、博士生导师，享受政府特贴专家。主要从事李群与微分几何的研究，已经在Advances in Mathematics, Crelle's Journal, Transactions AMS等杂志上发表100多篇研究论文，独立撰写的专著《Homogeneous Finsler Spaces》2012年由Springer出版社纽约分社出版，列入著名数学专著系列 Springer Monographs in Mathematics 中。2003年入选教育部优秀青年教师资助计划，2004年入选新世纪优秀人才支持计划，2007年获宝钢全国优秀教师奖，2014年获全国高校自然科学二等奖（第一完成人），2015年获天津市教学名师奖，2016年获天津市五一劳动奖章，2020年被评为天津市劳动模范，2022年获霍英东教育教学二等奖。主持8项国家自然科学基金项目，其中重点项目一项。他是20132017和20182022年度教育部数学专业教学指导委员会委员。
A bialgebra theory for transposed Poisson algebras via antipreLie bialgebras
and antipreLiePoisson bialgebras
Speaker: Chengming Bai (南开大学陈省身数学研究所)
Time: August 13, 2024 15:0016:00
Venue: 吉林大学数学楼第5研讨室
Abstract: The approach for Poisson bialgebras characterized by Manin triples with respect to the invariant bilinear forms on both the commutative associative algebras and the Lie algebras is not available for giving a bialgebra theory for transposed Poisson algebras. Alternatively, we consider Manin triples with respect to the commutative 2cocycles on the Lie algebras instead. Explicitly, we first introduce the notion of antipreLie bialgebras as the equivalent structure of Manin triples of Lie algebras with respect to the commutative 2cocycles. Then we introduce the notion of antipreLie Poisson bialgebras, characterized by Manin triples of transposed Poisson algebras with respect to the bilinear forms which are invariant on the commutative associative algebras and commutative 2cocycles on the Lie algebras, giving a bialgebra theory for transposed Poisson algebras. This is a joint work with Guilai Liu.
Bio: 白承铭，南开大学陈省身数学研究所教授，所长，南开大学副校长，国务院学位委员会第八届学科评议组成员，教育部核心数学与组合数学重点实验室主任，物理中的群论方法国际大会常务委员会委员。主要从事与数学物理和李理论相关的一些代数体系的结构及其应用的研究。曾获国家杰出青年基金资助和国务院政府特殊津贴，并入选国家“万人计划”科技创新领军人才。培养博士生和硕士生多名，其中的倪翔曾获中国数学会“钟家庆数学奖优秀硕士论文奖”。
Symplectic Morse Theory and Witten Deformation
Speaker: Xiang Tang (美国圣路易斯华盛顿大学)
Time: August 08, 2024 9:0010:00
Venue: ZOOM ID：904 645 6677, Password：2024
Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456
Abstract: In this talk, we will introduce a Morse type cohomology for symplectic manifolds using gradient flows and integration of the symplectic form over spaces of gradient flow lines. We will study this symplectic Morse cohomology using the Witten deformation method. In particular, we will explain that the symplectic Morse cohomology is isomorphic to the cohomology of differential forms introduced by Tsai, Tseng, and Yau for symplectic manifolds. This talk is based on joint works with David Clausen and LiSheng Tseng.
Bio: 唐翔，美国圣路易斯华盛顿大学数学系教授。北京大学数学学院2000届本科毕业生。2004年在美国加州大学Berkeley分校数学系取得博士学位。2023年当选AMS Fellow。
Quantum symmetric spaces and Sklyanin determinants
Speaker: Naihuan Jing (North Carolina State University)
Time: July 14, 2024 9:3010:30
Venue: 吉林大学正新楼209
Abstract: We study the invariant theory of quantum symmetric spaces of symplectic and orthogonal types. Explicitly the quantum symmetric spaces are realized as subrings of the quantum coordinate ring $M_q(N)$ where the relations are given by the quantum minors, Sklyanin determinants, and quantum Pfaffians. One of our results points out that the square of root of quantum determinant is essentially the Sklyanin determinant in a special case, answering a question of Noumi. This is joint work with Jian Zhang(张健).
Bio: 景乃桓，耶鲁大学博士，北卡州立大学终身教授。主要从事无限维李代数、量子群、表示论、代数组合和量子计算方面的研究工作。景乃桓教授在对称函数方面的研究成果被国际上命名为“景氏算子”,在国际主要数学刊物上发表近百篇论文，编辑著作5部。
Symplectic and Contact Geometry of Monge– Ampère equation: Introduction and application
Speaker: Vladimir Rubtsov (Université d’Angers, ITTP Moscow and IGAP Trieste)
Time: June 27, 2024 20:0021:00
Venue: ZOOM ID：904 645 6677, Password：2024
Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456
Abstract: I will present an introduction to the geometric approach to Monge–Ampère operators and equations based on contact and symplectic structures of cotangent and the 1st jet bundles of a smooth manifold. This approach was developed by V. Lychagin and goes back to the ideas of E. Cartan and his successor T. Lepage. I shall try to make my talk selfcontained. I also plan to discuss various applications and links with important geometric structures.
Bio: Vladimir Rubtsov graduated in Mathematics from the Moscow State University in 1974 with a MSc in Differential Geometry and Applications. He has a PhD in Higher Geometry and Topology (1983) and held research and teaching positions at various Mathematics and Applied Mathematics Laboratories in the former Soviet Union. Presently he is Professor at the Department of Mathematics, Université d'Angers, and a member of LAREMA (Anjou Research Mathematical Laboratory) of CNRS (France). His research is in the area of Poisson geometry, quantum Groups, integrable systems, symplectic and contact geometric methods in nonlinear differential equations and applications in hydrodynamics.
Integrable Peakon Models and Beyond
Speaker: Zhijun Qiao (University of Texas Rio Grande Valley)
Time: June 22, 2024 16:0017:00
Venue: ZOOM ID：904 645 6677, Password：2024
Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456
Abstract: In this talk, we will introduce integrable peakon models developed in recent years and present a basic approach how to get the peakon solutions of integrable equations. In particular, the CH peakon equation is extended to the bfamily quadratic and cubic peakon models (FORQ, MOCH, Novikov Equations etc) with peakon and weakkink solutions. We will also talk about a new CHtype equation – fifthorder CH equation and present new type solutions – pseudopeakon solutions and their interactions. Some work in the talk is joint with Dr. BQ Xia and Dr. E Reyes. Open problems are proposed in the end for discussion.
Bio: 乔志军教授于1997年获得复旦大学数学系博士学位，从师谷超豪院士和胡和生院士。1997 1999在北京大学数学学院做博士后。 1999年获得百篇优秀博士毕业论文。19992001，德国洪堡基金获得者。现任美国德克萨斯大学数学学院讲席教授，研究方向是非线性偏微分方程，可积系统与非线性尖孤波，KdV方程和孤立子理论，可积辛映射，R矩阵理论，雷达图像处理和数学物理的反问题。现已出版著作2部，发表论文180余篇，其中包括著名国际杂志《数学物理学通讯》、《非线性科学》等。现作为项目负责人已经完成20多个国家和国际科研项目。组织超过20个国际会议、研讨会。担任国际权威期刊《Studies in Applied Mathematics》编委，以及《Journal of Nonlinear Mathematical Physics》主编。
一类形变李代数的结构与表示
Speaker: 郜云 (加拿大约克大学)
Time: June 18, 2024 15:3016:30
Venue: 吉林大学正新楼209
Abstract: 扭HeisenbergVirasoro代数是一类重要的无限维李代数，它与一类曲线的模空间有关。我们对这一李代数的结构与表示进行了系统的研究。
Bio: 郜云，加拿大约克大学教授，德国洪堡学者。主要研究兴趣是高维仿射李代数及相关代数的结构与表示理论。
Hopf trusses an related structures in a monoidal setting
Speaker: Ramón González Rodríguez (University of Vigo)
Time: May 09, 2024 20:0021:00
Venue: ZOOM ID：904 645 6677, Password：2024
Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456
Abstract: The main topic of this talk are certain algebraic structures that in recent years have received attention from numerous mathematicians. More concretely, in this talk we will present, in a braided monoidal setting, the main properties and categorical relationships between the categories of Hopf trusses, weak twisted postHopf algebras and weak twisted relative RotaBaxter operators. The latter objects are a generalisation of the relative RotaBaxter operators where the RotaBaxter condition is modified through a cocycle. Also we will present the notion of generalized invertible 1cocycle and we prove that the category of Hopf trusses is equivalent to the category of generalized invertible 1cocycles. On the other hand, we also introduce the notions of module for a Hopf truss and for a generalized invertible 1cocycle. We prove some functorial results involving these categories of modules and we show that the category of modules associated to a generalized invertible 1cocycle is equivalent to a category of modules associated to a suitable Hopf truss. Finally, assuming the existence of equalizers, we introduce the notion of Hopfmodule in the Hopf truss setting and we obtain the Fundamental Theorem of Hopf modules associated to a Hopf truss.
Bio: Ramón González Rodríguez is a full professor at the Departament of Applied Mathematics II in the University of Vigo. His research interests is centered on Hopf algebras and and their generalizations as, for example, weak Hopf algebras, Hopf quasigroupos, groupoids, quasigroupoids, Hopf braces and Hopf trusses. His home page is https://dma.uvigo.es/~rgon/
Mathematics of Imaging Modalities Using Resonant Contrast Agents
Speaker: Mourad Sini (Austrian Academy of Sciences)
Time: May 0817, 2024
Venue: 正新楼106教室
Introduction: In these lecture, we describe mathematical modeling and analysis of imaging modalities using resonant contrast agents that were recently proposed and highly investigated in the applied engineering community. We offer an original approach to state and solve a family of inverse problems that originate from such imaging modalities.
We start by motivating the need of using contrast agents in imaging (but also in the drugs delivery and therapy modalities at large) and highlight why their resonant effect is the key feature. We describe the close link between the contrast properties of these agents and the classes of resonant frequencies they can generate. These resonant frequencies are characterized as scattering resonances (i.e. generalized eigenvalues) of the related operators. In addition, they are the only frequencies for which the resolvent of this operator is not trivial (does not coincide with the one of the background one, called the free operator). For those resonant frequencies, this resolvent is nothing but the one of the pointsupported singular perturbations of the free operator. This pointlike perturbation is given as pointsource to which is attached a scattering coefficient modeling the interaction between the contrast agent and the surrounding background. In addition, this scattering coefficient reaches its maximum, as a function of the frequency, at the (dominant real part) of the resonant frequencies.
As a consequence of this second characterization, these resonant contrast agents considerably amplify any incident wave (or source) sent at frequencies close to their resonances. This allows to perform quantitative estimates of the background medium using remote measurements. Following this approach, we describe recent results obtained in the frameworks of Ultrasound, Optic and PhotoAcoustic imaging.
Two scenarios are discussed here. In the first one, we use isolated (or closelyspaced) contrast agents. Two general ideas can be highlighted in this case depending whether we use timeharmonic or time domain measurements:
1. Timeharmonic case. Looking at the measured fields in terms of the incident frequencies, we can recover the related resonances (as the Minnaert or the plasmonic resonances). These resonances have signatures of the background surrounding the location of the used contrast agent.
2. Timedomain case. Looking at the measured fields in terms of time, we can recover the internal values of the traveltime function. This traveltime function provides us the values of the speed of propagation by solving the Eikonal equation.
In the second scenario, these agents are used allatonce, as a cluster. In this case, we show that we can linearize the boundary maps, as the NeumannDirichlet maps, using incident frequencies close to the related resonances. In addition, we derive explicit reconstruction formulas of the medium which enjoy improved stability estimates for the detection. Therefore, using resonant perturbations, we get rid of the nonlinear character and the instability issue of the detection using remote measurements which are the two most inherent drawbacks in using traditional (i.e. contrast agents free) repeated remote measurements.
Finally, as the proposed approach is flexible enough, we describe a larger family of imaging modalities that can fit into the framework and show to what extent we can solve the related inverse problems.
Schedule:
Bio: M. Sini got his PhD degree from University of Provence, France, in October 2002. From September 2006, he joined the Radon Institute, of the Austrian Academy of Sciences, where he was tenured since 2011 as a senior fellow (equivalent to university professor) after securing the Habilitation degree from J. Kepler University in 2009. M. Sini was invited to deliver the IAAM Award Lecture (Sweden, August 2019) and an invited plenary speaker in the Applied Inverse Problems (AIP) conference (Grenoble, France, July 2019). He attracted around 2 Mi euro as thirdparty funding. M. Sini is interested in the analysis of partial differential equations applied to inverse problems, mathematical imaging, mathematical therapy and material theory. By now, he published nearly 100 papers, most of them in top journals, several book chapters and coedited a book. He is member of the editorial board of several journals including Mathematical Methods in Applied Sciences (Wiley) and Communication on Analysis and Computation (AIMS).
LAlgebras: The YangBaxter equation in algebraic logic
Speaker: Leandro Vendramin (Vrije Universiteit Brussel，Belgium)
Time: April 23, 2024 20:0022:00
Venue: ZOOM ID：904 645 6677, Password：2024
Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456
Abstract: We will discuss interactions between settheoretical solutions to the YangBaxter equation and structures that appear in algebraic logic. Most of this interplay will be based on the recently introduced theory of Lalgebras. Hilbert and Heyting algebras are examples of Lalgebras. The talk requires almost no background. We will present examples, problems and conjectures.
Bio: Leandro Vendramin is an Associate Professor of Mathematics at the Vrije Universiteit Brussel, Belgium. His research interests are related to the algebra behind the YangBaxter equation. This includes Hopf algebras and Nichols algebras and discrete structures such as skew braces and Lalgebras. His home page is https://leandrovendramin.org.
A gentle introduction to the Drinfel'd associator
Speaker: Martin Bordemann (Université de Haute Alsace, Mulhouse, France)
Time: April 11, 2024 20:0021:00
Venue: ZOOM ID：904 645 6677, Password：2024
Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=87511211646
Abstract: This is a pedagogical talk about the famous associator invented by V.G.Drinfel'd in 1989/90 and a proof of its hexagon and pentagon identities. It is wellknown that this associator has applications to the quantization of (quasi) Lie bialgebras (P.I.EtingofD.A.Kazhdan and B.EnriquezG.Halbout), deformation quantization (D.E.Tamarkin) and number theory (multiple zeta values) via its rôle in deforming symmetric monoidal categories into braided ones using an `infinitesimal braiding'. Drinfel'd's exposition in the original articles (but also the one in most textbooks) had been quite sketchy, and the mortal reader usually does not know to what extent s/he has to know deep complex analysis, algebraic topology, or conformal field theory. We give a much more elementary and explicit approach using limits of (formal) parallel transports along concrete paths in explicit starshaped domains of the real line and plane with respect to explicit flat (formal) connections derived from the KnizhnikZamolodchikov connection.
Bio: Martin Bordemann is presently a full professor at the mathematics department of the Université de Haute Alsace, Mulhouse, France since 2000. He has done a PhD in mathematical physics on integrable systems with Hartmann Römer in Freiburg, Germany (1990) and a Master of mathematics with Otto Kegel in Freiburg on metrised Lie algebras (1989). His research is centered around deformation quantization, and more general algebraic deformation theory.
A Combinatorial Approach to Homology of Algebraic Systems
Speaker: Viktor Lopatkin (Higher School of Economics)
Time: April 06, 2024 16:0017:00
Venue: ZOOM ID：904 645 6677, Password：2024
Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=87511211646
Abstract: It is well known there are many important algebras, groups, semigroups are presented via generators and relations. In other words, we get a set of generators and relations among them. It then arises a question is about relations among relations, relations among relations among relations and so on. It thus gives a “natural” way for appearing of resolutions. This is a homological algebra point of view to study such algebraic structures. In this talk we will get to know about a power and universal method how to construct such resolutions which are call Anick resolutions. This method is based on two big foundations; GroubnerShirshov bases theory and algebraic discrete Morse theory. We consider how it works in some examples (symmetric group S3) and we also talk about comultiplication of Anick complexes which give arise to multiplication on cohomology.
Bio: Viktor Lopatkin is an associate professor at HSE University (=Higher School of Economics) in Moscow, Russia. He works at Anick resolutions and GroubnerShirshov bases theory. He also takes an interest at knot theory, vertex algebra theory, Lie algebra theory.
Skew braces and related structures
Speaker: Senne Trappeniers (Vrije Universiteit Brussel)
Time: March 28, 2024 20:0022:00
Venue: ZOOM ID：904 645 6677, Password：2024
Abstract: Historically, (skew) braces are algebraic structures that arose out of the study of settheoretic solutions of the YangBaxter equation. Braces were defined by Rump in 2006 and skew braces by Guarnieri and Vendramin in 2017. They provide a nice framework to formulate some older results of Etingof, Schedler, Soloviev regarding the YangBaxter equation, but also provide new constructions and insights. Since these seminal papers, research around skew braces has both improved the understanding of their interplay with the YangBaxter equation, but also unveiled unexpected connections with for example HopfGalois extensions, preLie rings and postLie algebras. In this talk, the goal is to give an overview of some of these connections and state related open research questions.
Bio: Senne Trappeniers is PhD student at the Vrije Universiteit Brussel under supervision of Leandro Vendramin. His research interests are centered around skew braces, ranging from purely skew brace theoretic questions to connections with other mathematical structures like HopfGalois extensions, settheoretic solutions of the YangBaxter equation and preLie rings.
RotaBaxter operators on groups
Speaker: Aleksei Galt (Sobolev Institute of Mathematics)
Time: March 21, 2024 15:3016:30
Venue: The fifth seminar room, Mathematics Building
Abstract: RotaBaxter operators on Lie groups and more generally on groups were introduced by Guo, Lang, and Sheng in 2021. In this talk we discuss some general constructions of RotaBaxter operators on groups. We describe all RotaBaxter operators on dihedral and alternating groups.
Bio: Aleksei Galt is a senior researcher of Sobolev Institute of Mathematics and an associate professor of Novosibirsk State University. He finished his PhD thesis “Conjugacy problems in finite groups of Lie type” in 2010. His research interests are finite groups of Lie type, linear algebraic groups, permutation groups and related areas.
Lie brackets on affine spaces
Speaker: Tomasz Brzeziński (Swansea University and University of Białystok)
Time: March 07, 2024 20:0022:00
Venue: ZOOM ID：904 645 6677, Password：2024
Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=87511211646
Abstract: We first explore the definition of an affine space which makes no reference to the underlying vector space and then formulate the notion of a Lie bracket and hence a Lie algebra on an affine space in this framework. Since an affine space has neither distinguished elements nor additive structure, the concepts of antisymmetry and Jacobi identity need to be modified. We provide suitable modifications and illustrate them by a number of examples from matrix algebra and geometry.
Bio: Tomasz Brzeziński is a Professor of Mathematics at Swansea University (UK) and University of Białystok (Poland). He is a mathematician specialising in Algebra (in particular studies of various algebraic structures such as rings, modules, corings, comodules, Hopf algebras etc.), Noncommutative Geometry (both algebraic and differential, with particular stress put on symmetry aspects), Category Theory and some aspects of Mathematical Physics (quantum groups, integrable systems). He is the author or coauthor of a monograph and over 110 papers (written with ca 45 coauthors). One of his notable achievement is the revival and significant development of the theory of corings (new AMS classification category has been created for corings and comodules as a result of this activity).
Compatible Poisson structures on multiplicative quiver varieties
Speaker: Maxime Fairon (Université de Bourgogne)
Time: February 29, 2024 20:0022:00
Venue: ZOOM ID：904 645 6677, Password：2024
Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=87511211646
Abstract: Any multiplicative quiver variety is endowed with a Poisson structure constructed by M. Van den Bergh through reduction from a Hamiltonian quasiPoisson structure. The smooth locus of this variety carries a corresponding symplectic form defined by D. Yamakama through quasiHamiltonian reduction. In this talk, I want to explain how to include this Poisson structure as part of a larger pencil of compatible Poisson structures on the multiplicative quiver variety. The pencil is defined by reduction from a pencil of (nondegenerate) Hamiltonian quasiPoisson structures, whose construction can be adapted to various frameworks, e.g. in relation to character varieties. I will start by explaining the simpler analogous situation that leads to a pencil of Poisson structures on (additive) quiver varieties, before detailing the multiplicative case. Moreover, I will show that it is possible to understand the construction through the lens of noncommutative Poisson geometry. Time allowing, I may comment on the application of this result to the spin RuijsenaarsSchneider phase space; this shows the compatibility of two Poisson structures that appeared in independent works of ArutyunovOlivucci (arXiv:1906.02619) and of Chalykh and myself (arXiv:1811.08727).
Bio: Maxime Fairon is Maître de Conférences (equivalent to lecturer) at Institut de Mathématiques de Bourgogne, Université de Bourgogne, Dijon, France. His research interests are split between: i) classical integrable systems appearing in mathematical physics, and ii) noncommutative Poisson geometry.
Modular classes in Poisson and Jacobi geometry
Speaker: Aissa Wade (Penn State University, USA)
Time: February 22, 2024 21:0022:00
Venue: ZOOM ID：904 645 6677, Password：2024
Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=87511211646
Abstract: The modular class of a Poisson manifold is an element of its first Poisson cohomology group, which measures the obstruction to the existence of a measure on this Poisson manifold that is invariant under all Hamiltonian diffeomorphisms The concept of a modular class was extended to general Lie algebroids by Evens, Lu and Weinstein. Recently, there have been various developments and applications of modular classes of Poisson manifolds and Lie algebroids. The main goal of this talk is to introduce modular classes in the more general setting of Jacobi geometry. We will first give a brief review of modular classes in Poisson geometry, and then we will discuss Jacobi manifolds, Jacobi algebroids, and Gerstenhaber Jacobi algebras. Finally, we will introduce modular classes of Jacobi manifolds and Jacobi algebroids.
Bio: Aissa Wade is a professor in the Mathematics Department at Penn State University. She was the Head of the African Institute for Mathematical Sciences (AIMS) center in Senegal from 2016 to 2018. Her research interests lie in Poisson geometry, contact geometry and mathematical physics.
Free postgroups, postgroups from group actions and postLie algebras
Speaker: Dominique Manchon (Université ClermontAuvergne)
Time: February 01, 2024 20:0021:00
Venue: ZOOM ID：904 645 6677, Password：2023
Link: https://us02web.zoom.us/j/9046456677?pwd=UHErd3RJVzFsNzNnczFZYm9uYlV6QT09
Abstract: After providing a short review on the recently introduced notion of postgroup by C. Bai, L. Guo, Y. Sheng and R. Tang, we will exhibit postgroup and weak postgroup counterparts of important postLie algebras in the literature, including the infinitedimensional postLie algebra of Lie group integrators. The notion of free postgroup will be examined, and a group isomorphism between the two group structures associated to a free postgroup, reminiscent to A. Gavrilov's Kmap in differential geometry, will be described. This is a joint work with Mahdi Jasim Hasan AlKaabi (Mustansiriyah University, Baghdad, Iraq) and Kurusch EbrahimiFard (NTNU, Trondheim, Norway).
Bio: Dominique Manchon Chargé de Recherches (senior researcher) at CNRS, Laboratoire de Mathématiques Blaise Pascal, Université ClermontAuvergne, ClermontFerrand, France. His research interests are Lie groups and Lie algebras, Hopf algebras and algebraic combinatorics.
Finite generations of Yoneda algebras for complete intersections
Speaker: Zongzhu Lin (Kansas State University)
Time: January 25, 2024 9:0011:00
Location: ZOOM ID：904 645 6677, Password：2023
Link: https://us02web.zoom.us/j/9046456677?pwd=UHErd3RJVzFsNzNnczFZYm9uYlV6QT09
Abstract:
Bio: 林宗柱，美国堪萨斯州立大学终身教授，博士生导师，曾任三峡数学研究中心主任，美国科学基金会NSF项目主任和《中国科学：数学》编委。主要从事表示论、代数群以及量子群等方面的研究，论文发表在 Invent. Math., Adv. Math., Trans. Amer. Math. Soc., CMP 和J. Algebra 等重要学术期刊上。
Parametrizations of algebraic structures
Speaker: Loic Foissy (Université du Littoral Côte d’Opale (ULCO), Calais, France)
Time: January 11, 2024 20:0021:00
Location: ZOOM ID：904 645 6677, Password：2023
Abstract: In the last few years, several generalizations of classical objects (associative, dendriform, preLie, RotaBaxter algebras and others) appear in the literature. In each case, each product is replaced by a family of products indexed by a set (matching objects) or by a semigroup (family objects), with axioms mimicking the classical one in such a way that, loosely speaking, the underlying combinatorics is conserved.
We shall give a way to include all these generalizations in a same frame. This will make appear algebraic structures on the set used for the parametrization, such as extended (di)associative semigroups, which are (di)associative semigroups with extra products.
This is a joint work with Dominique Manchon, XiaoSong Peng and Yuanyuan Zhang.
Bio: Loic Foissy is a professor at the University of the Littoral Cote d’Opale, France. His research domain is Algebraic Combinatorics. More precisely, He works on combinatorial Hopf algebras, operads and their applications.
Can AI do mathematical research?
Speaker: Nguyen Tien Zung (University of Toulouse, France and Torus AI)
Time: December 7, 2023 20:0021:00
Location: ZOOM ID：904 645 6677, Password：2023
Abstract: In this talk I would like to discuss the question: Can AI (artificial intelligence) do mathematical research, create new beautiful and useful mathematical theories, solve longstanding math problems, and explain all that in an easy to understand way to humans? What are the steps towards building such an AI? What will be the implications for us mathematicians? I will begin the talk by a brief survey of what can AI do for mathematics right now, with examples in problem solving, dynamical systems, etc.
Bio: Nguyen Tien Zung is a pure mathematician turned AI entrepreneur, professor at the University of Toulouse (on leave), founder of the startup Torus AI.
RotaBaxter operators and coboundary Lie bialgebra structures on perfect finitedimensional Lie algebras
Speaker: Maxim Goncharov (Sobolev Institute of Mathematics)
Time: December 1, 2023 13:0014:00
Location: 313 Zhengxin Building
Abstract: There is a connection between structures of a Lie bialgebra on a given quadratic Lie algebra L and RotaBaxter operators of a special type on L. Namely, there is a classical result that says that structures of a triangular Lie bialgebra on a quadratic Lie algebra L are in onetoone correspondence with skewsymmetric RotaBaxter operators of weight zero on L. Another classical result states the connection between factorizable Lie bialgebra structures and RotaBaxter operators of weight 1 satisfying some generalized skewsymmetry property. In this talk, we will generalize these results and speak on the connection between coboundary Lie bialgebra structures on a perfect quadratic Lie algebra with solutions of the modified classical YangBaxter equation and RotaBaxter operators of special type. Also, we will describe the classical double of a coboundary Lie bialgebra in terms of RotaBaxter operators. As an application, we will speak on coboundary Lie bialgebra structures on simple, semisimple, and reductive finitedimensional Lie algebras.
Bio: Maxim Goncharov, Ph.D., Senior research fellow in Sobolev Institute of Mathematics, Associate Professor at Novosibirsk State University.
Solving some Hamiltonian system via the inverse scattering method
Speaker: Xiaomeng Xu (Peking University)
Time: December 1, 2023 11:0012:00
Location: 313 Zhengxin Building
Abstract: The inverse scattering method, as well as the rmatrix formulation, was designed to study some nonlinear problem via the associated linear one. This talk studies a question of this type. In particular, it finds some special solutions of the Hamiltonian system arising from the theory of isomonodromy deformation.
Bio: 徐晓濛，北京大学助理教授，2016年获日内瓦大学博士学位，主要研究方向是表示论、辛几何、奇点理论及其在数学物理中的应用。目前在Adv. Math., Comm. Math. Phys., Int. Math. Res. Not. 等数学期刊发表多篇论文。
The descriptions of solvable Lie superalgebras of maximal rank
Speaker: Bakhrom Omirov (National University of Uzbekistan)
Time: November 30, 2023 13:3014:30
Location: 313 Zhengxin Building
Abstract: This report is devoted to the study of the structures of complex Lie superalgebras of maximum rank. Under certain conditions, we will give estimates for upper bounds on the dimensions of subspaces complementary to nilradicals and show that an arbitrary solvable Lie superalgebra of maximal rank is isomorphic to a maximal solvable extension of a nilradical of maximal rank. Some other additional results related to cohomology groups of solvable Lie algebras of maximum rank will be discussed.
Bio: Bakhrom Omirov is a professor at the National University of Uzbekistan. His research focused on nonassociative algebras and superalgebras. In particular, he is one of the authors of the monograph devoted to the structure theory of Leibniz algebras. Bakhrom Omirov is a member of The World Academy of Sciences, which includes 66 countries), as well as Uzbek and American Societies.
He is a winner of several prestigious fellowships (Fulbright, USA; INTAS, Belgium).
Graded geometry and applications in physics
Speaker: Vladimir Salnikov (CNRS / La Rochelle University)
Time: November 30  December 1, 2023
Location: 313 Zhengxin Building
Schedule:
Abstract: In this minicourse I will give an overview of results on various instances of graded geometry, that we have obtained with several colleagues in the last years. I will start with a comparison of definitions of N and Z graded manifolds and introduce a way of constructing a filtration of the sheaf of function on the latter one. Then I will turn to differential graded manifolds (also called Qmanifolds) and present a normal for result for a homological vector field on Zgraded manifold. Related constructions have been applied in theoretical physics, namely for studying symmetries and gauging of sigma models  I will comment on that. And in the end I will present one of my motivations to going through the labor of all these construction: the problem of integration of differential graded Lie algebras and some ongoing projects inspired by it.
Bio: Vladimir Salnikov is a researcher at CNRS (National Centre for Scientific Research), La Rochelle University, France. His scientific interests are graded and generalized geometry, dynamical systems, applications to mechanics and theoretical physics.
Syzygy modules and simplicial resolutions
Speaker: Aliaksandr Hancharuk (University Lyon 1)
Time: November 1316, 2023 21:0022:00
Location: Zoom id：904 645 6677 Password：2023
Abstract: Hilbert in 1890s famously proved that a graded finitely generated module over a polynomial ring admits a free resolution of finite length. Since then a lot of progress has been done on the structure and properties of finite free resolutions. We will study those underlying some abstract simplicial complex. Lastly, we relate these finite resolutions to the infinite ones and discuss its applications. Based on "Combinatorial commutative algebra" by Miller and Sturmfels, "Graded Syzygies" by Peeva and some new results by the author.
Four subtitles of the minicourse:
1. Graded free resolutions. Koszul complex. Hilbert Syzygy theorem.
2. Simpicial resolutions, Taylor complex, Scarf complex.
3. Duality for resolutions, Alexander duality.
4. Infinite graded resolutions. Tate resolutions.
Bio: Aliaksandr Hancharuk did his Ph.D. in 2023 with Prof.Strobl in University Lyon 1. His research interests and work is concentrated in the intersection of mathematical physics and homological algebra, namely in the algebraic aspects of gauge theories.
Option Pricing with Transaction Costs: Challenges and Approaches
Speaker: Xiaoping Lu (University of Wollongong)
Time: November 9, 2023 10:0011:00
Location: 数学楼第二报告厅
Abstract: In modern finance, mathematics assumes a pivotal role, particularly in option pricing. However, the consideration of transaction costs introduces a complexity that the conventional notion of a unique fair price between the option holder and writer, no longer exists. Both parties now seek to recover the costs incurred through trading the underlying stocks as part of their hedging strategy, thereby influencing the prices at which they are willing to transact for options. Mathematically, transaction costs make the pricing problem much more complicated, especially for American options. In this talk, some methods we used to price options in the presence of transaction costs will be presented, providing insights into how transaction costs impact option prices and optimal exercise policies for American options.
Bio: Dr. Xiaoping Lu is an Associate Professor in Applied Mathematics and the Director of the Centre for Financial Mathematics at the School of Mathematics and Applied Statistics, University of Wollongong, Australia. Holding a PhD from the University of Michigan, Ann Arbor, USA, Xiaoping’s research journey is marked by a diverse range of interests, with a recent emphasis on financial mathematics. Her recent works have revolved around the valuation of American options and a spectrum of financial derivatives, including Barrier option, convertible bonds, Foreign Exchange, Interest Rate Derivatives, Timer Options, Parisian Options, Stock Loans, and Weather Derivatives. In addition to her publications in topranked international journals, Xiaoping has coedited a special issue on Financial Mathematics and Quantitative Finance for the ANZIAM Journal. She is also an editor at the International Journal of Mathematics for Industry.
Nilpotent Lie algebras with quadratic pseudoHermitian metrics
Speaker: Ignacio Bajo (Universidad de Vigo, Spain)
Time: October 26, 2023 20:0021:00
Location: Zoom ID：904 645 6677 Password：2023
Abstract: We study nilpotent Lie algebras endowed with a complex structure and a quadratic structure which is pseudoHermitian for the given complex structure. We propose several methods to construct such Lie algebras and use a method of double extension by planes to get an inductive description of all of them. Such a method let us give a complete classification of nilpotent quadratic Lie algebras where the metric is LorentzHermitian and to obtain a complete classification of pseudoHermitian quadratic Lie algebras up to dimension 8 and their inequivalent pseudoHermitian metrics.
Bio: Ignacio Bajo works at the Departament of Applied Mathematics II in the University of Vigo and currently the Chair of the Department. His research interests nowadays are focused on Lie algebras and Lie groups but also on other nonassociative algebras related to geometrical problems.
Stochastic anticipating equations
Speaker: Andrey Dorogovtsev (Institute of Mathematics，NAS Ukraine)
Time: October 23  November 14, 2023
Location: Zoom ID：871 7544 9382 Password：959182
Abstract: This course is devoted to the stochastic anticipating equations with the extended stochastic integral with respect to the Gaussian processes of a special type. Professor Andrey will give students some time to understand the knowledge and give some small questions about the lectures.
Schedule:
Bio: Andrey Dorogovtsev教授是乌克兰国家科学院通讯院士，乌克兰国家科学院数学所随机过程理论系主任，主要从事概率论及其相关领域研究，是乌克兰概率论研究方向学术领军人物之一。Andrey Dorogovtsev教授是乌克兰与德国、乌克兰与俄罗斯等国家联合项目的乌方负责人。同时，Andrey Dorogovtsev教授是《Theory of Stochastic Processes》、《Ukraine Mathematical Journal》等杂志的编委。
Perturbative expansion of YangBaxter operators and Lie algebra cohomology
Speaker: Emanuele Zappala (Idaho State University)
Time: October 19, 2023 20:0021:00
Location: Zoom ID：904 645 6677 Password：2023
Abstract: Selfdistributive objects in symmetric monoidal categories are known to produce YangBaxter operators, e.g. quandles and their linearization in modules. An important class of selfdistributive objects arises from Lie algebras (binary and $n$ary as well), giving a way of constructing a YangBaxter operator from an initial Lie algebra. This allows us to study the relation between selfdistributive cohomology, Lie algebra cohomology, and YangBaxter cohomology. We therefore obtain a theory of infinitesimal deformations of YangBaxter operators that is tightly connected to the deformation theory of Lie algebras and their associated selfdistributive objects. In this talk, I will explore these connections and the results that can be shown in this regard. Moreover, I will consider the problem of obtained higher order deformations of the YangBaxter operators in relation to the higher deformations of Lie algebras, therefore producing YangBaxter operators that are given by a formal power series (perturbative expansion). I will also present several open questions.
Bio: Emanuele Zappala is an assistant professor in the department of Mathematics and Statistics at Idaho State University. His work mainly concerns quantum algebra (YangBaxter operators and their cohomology), geometric topology (cohomological invariants of embedded surfaces), applications of algebra and topology to quantum machine learning, and operator learning (iterative methods in deep learning).
Higher order algebroids and representations up to homotopy
Speaker: Mikołaj Rotkiewicz (University of Warsaw. Institute of Mathematics )
Time: September 27, 2023 20:0021:00
Location: Zoom ID: 904 645 6677 Password:2023
Abstract: The concept of a higher algebroid, as introduced by M. Jóźwikowski and M. Rotkiewicz, naturally generalizes the notions of an algebroid and a higher tangent bundle. The idea is based on a description of (Lie) algebroids as differential relations of a special kind. My goal is to explain the notion of a higher algebroid in a more standard language, i.e. in terms of some bracket operations and vector bundle morphisms. In order two we end up with representation up to homotopy of (Lie) algebroids.
Bio: Mikołaj Rotkiewicz is an academic teacher and a researcher in the Faculty of Mathematics, Informatics and Mechanics in Warsaw. He obtained PhD in the field of Lie groups and Lie algebras. He was granted a fellowship from the Polish Academy of Sciences. Earlier he was awarded in many mathematical competitions. He is an author of a dozen publications in prestigious journals. His mathematical interest lies in graded geometry, theory of supermanifolds, geometric mechanics and recreational mathematics.
Construction of nilpotent Lie algebras with complex structures
Speaker: Adela Latorre (Polytechnic University of Madrid, Spain)
Time: September 21, 2023 17:0018:00
Location: Zoom ID: 904 645 6677 Password:2023
Abstract: Complex manifolds can be characterized as pairs (M,J), where M is an evendimensional differentiable manifold and J is a complex structure on it. Although the explicit construction of these J's is a difficult task, the problem can be slightly simplified when M is a nilmanifold and one restricts to the study of invariant complex structures on M. In this case, the problem of finding the pairs (M,J) is related to the classification of real nilpotent Lie algebras with complex structures. Such classification has been completed in real dimensions 4 and 6. However, the same techniques are difficult to apply when the dimension of the nilpotent Lie algebra is equal to or higher than 8. In this talk, we will present a new approach to the problem that will allow us to find every 8dimensional real nilpotent Lie algebra having onedimensional center and admitting complex structures.
Bio: Adela Latorre works at the Department of Applied Mathematics of the Polytechnic University of Madrid (Spain). Her main research area is complex nonKähler geometry, although she is also interested in topics related to Lie algebras and Lie groups.
PreLie algebra structures and etale affine representations
Speaker: Dietrich Burde (University of Vienna, Austria)
Time: September 14, 2023 20:0021:00
Location: Zoom ID: 904 645 6677 Password:2023
Abstract: PreLie algebras and PostLie algebras arise in many areas of mathematics and physics. They are also related to etale affine representations of Lie algebras and algebraic groups. They also arise in the context of affine geometry on Lie groups, operad theory, deformation theory and YoungBaxter equations. For reductive groups, every etale affine representation is equivalent to a linear representation and we obtain a special case of a prehomogeneous representation. Such representations have been classified by Sato and Kimura in some cases. The induced representation on the Lie algebra level gives rise to a preLie algebra structure on the associated Lie algebra. PreLie algebra structures also correspond to leftinvariant affine structures on Lie groups. In this talk we present results on the existence of etale affine representations of reductive groups and Lie algebras and discuss a related conjecture of V. Popov concerning flattenable groups and linearizable subgroups of the affine Cremona group.
Bio: Dietrich Burde is a professor at the Department of Mathematics at the University of Vienna. He obtained his Ph.D. in 1992 at the University of Bonn in Germany. His research interests lie in algebra and geometry, in the area of Lie groups, Lie algebras, algebraic groups and representation theory. He has received research grants from the Austrian Science Foundation on the topic "Affine Geometry on Lie Groups and Liealgebraic Structures".
Semidirect products in digroups, skew braces, heaps, trusses, and in universal algebra
Speaker: Alberto Facchini (University of Padua)
Time: September 7, 2023 20:0021:00
Location: Zoom ID: 904 645 6677 Password:2023
Abstract: We will present some algebraic structures that have recently received attention in view of their relation with set theoretic solutions of the YangBaxter equation. We will present the basic properties of digroups, skew braces, heaps, and trusses. In particular, we will focus on their semidirect products.
Bio: Alberto Facchini has been full professor of Algebra until 1999 at the University of Udine, and from 1999 to 2022 at the University of Padua. Now he is an Emeritus Professor. He has had six PhD students and has written more than 170 research papers published in mathematical journals, four textbooks, and two research books published by Birkhäuser Verlag (Basel). He is a member of Accademia San Marco and Accademia Galileiana di Scienze Lettere ed Arti in Padova. He has given scientific communications and lectures in almost 40 different countries. He has been one of the editors of a dozen mathematical journals, among which Bollettino dell'Unione Matematica Italiana, Communications in Algebra, Journal of Algebra and Its Applications, Journal of the Egyptian Mathematical Society, and Rendiconti del Seminario Matematico dell'Università di Padova. In Udine he has been dean of the Faculty of Science, in Padua he has been director of the Department of Pure and Applied Mathematics.
Introduction to Noncommutative Isolated Singularities and Resolutions
Speaker: Quanshui Wu (Fudan University)
Time: August 23, 2023 10:3011:30
Location: 正新楼313室
Abstract: This will be an introductory talk to noncommutative isolated singularities and resolutions. I will recall some examples of commutative isolated singularities and noncommutative isolated singularities first. Then I will survey some related results, and introduce a version of noncommutative resolutions of commonly graded ASGorenstein singularities.
Bio: 吴泉水，复旦大学数学科学学院教授、博导、上海数学中心执行主任，主要从事非交换环论、非交换射影代数几何、Hopf代数的同调理论方面的研究。曾获教育部科技进步二等奖、教育部霍英东教育基金会青年教师奖、教育部高校“青年教师奖”、宝钢优秀教师奖、上海市优秀学术带头人、上海市优秀青年教师等，在Duke Math. J.、Trans. Amer. Math. Soc.、Israel J. Math.、J. Noncommut. Geom.、J. Algebra、J. Pure Appl. Algebra等国际著名期刊发表SCI论文50余篇，多次主持国家自然科学基金面上项目，曾担任SCI杂志Comm. Algebra编委。
Noncommutative moduli spaces
Speaker: Andrey Lazarev (Lancaster University)
Time: August 2125, 2023
Location: 正新楼313室
Abstract: The aim of this minicourse is to outline the construction of global moduli spaces of different objects of algebraic and geometric nature (such as flat connections in vector bundles, modules over associative algebras, objects in dg categories etc.) in a homotopy invariant context. The first part of the course will explain how the local Koszul duality of Hinich and KellerLefevre provides a suitable context for studying local moduli problems (also known as deformations). The second part is devoted to the more recent work constructing the corresponding global theory. The global theory shares some properties with the local one but involves several significantly new features, most notably the use of dg categories. The emphasis will be placed on explaining the conceptual picture rather than on technical proofs. Various instructive examples will be given.
Bio: Andrey Lazarev，英国兰卡斯特大学教授，从事代数拓扑与同伦论的研究， Bull. Lond. Math. Soc.杂志主编，在Adv. Math.、 Proc. Lond. Math. Soc.、 J. Noncommut. Geom.等杂志上发表多篇高水平论文。
授课日期 Date of Lecture 
课程名称（讲座题目） Name (Title) of Lecture 
授课时间 Duration (Beijing Time) 
参与人数 Number of Participants 
Aug 21, 2023 
MaurerCartan (MC) elements and gauge transformations. Deformation theory 
10:3011:30 
30 
Aug 21, 2023 
Model categories and infinity categories, examples: dg algebras and dg Lie algebras 
16:3017:30 
30 
Aug 22, 2023 
Coalgebras and Liecommutative Koszul duality. 
10:3011:30 
30 
Aug 22, 2023 
Representability of deformation functors 
16:3017:30 
30 
Aug 24, 2023 
MC elements in dg associative algebras and associated dg categories. Homotopy gauge equivalences 
10:3011:30 
30 
Aug 24, 2023 
Homotopy theory of dg categories 
16:3017:30 
30 
Aug 25, 2023 
Global Koszul duality as a Quillen equivalence between infinitycategories of dg algebras and dg coalgebras 
10:3011:30 
30 
Aug 25, 2023 
Representability of noncommutative moduli space functors 
16:3017:30 
30 
On the volume of hyperbolic tetrahedron
Speaker: Nikolay Abrosimov (Sobolev Institute of Mathematics of RAS)
Time: August 20, 2023 10:3011:30
Location: 正新楼313室
Abstract: The talk will give an overview of the latest results on finding exact formulas for calculating the volumes of hyperbolic tetrahedra. The classical formula of G. Sforza [1] expresses the volume of a hyperbolic tetrahedron of a general form in terms of dihedral angles. Its modern proof is proposed in [2]. The formula in terms of edge lengths is obtained in the recent joint work of the author with B. Vuong [3]. The known formulas for the volume of a hyperbolic tetrahedron of a general form are very complicated and cannot always be applied to calculate the volumes of more complex polyhedra. So, a natural question arises to find more convenient and simple formulas for sufficiently wide families of hyperbolic tetrahedra. At the end of the talk, we will consider hyperbolic tetrahedra of special types: ideal, biorthogonal, 3orthogonal and their generalizations. The volume of the ideal and biorthogonal tetrahedron was known to N.I. Lobachevsky. We will present new formulas for calculating volumes and normalized volumes of a trirectangular hyperbolic tetrahedron [4] as well as its generalization for the 4parameter family of tetrahedra with one edge orthogonal to the face. The latter formulas can be used to calculate the volumes of more complex polyhedra in the Lobachevsky space.
References:
[1] G. Sforza, Spazi metricoproiettivi // Ricerche di Estensionimetria Integrale, Ser. III, VIII (Appendice), 1907, P. 41–66.
[2] N.V. Abrosimov, A.D. Mednykh, Volumes of polytopes in constant curvature spaces // Fields Inst. Commun., 2014, V. 70, P. 1–26. arXiv:1302.4919.
[3] N. Abrosimov, B. Vuong, Explicit volume formula for a hyperbolic tetrahedron in terms of edge lengths // Journal of Knot Theory and Its Ramifications, 2021, V. 30, No. 10, 2140007. arXiv:2107.03004.
[4] N. Abrosimov, S. Stepanishchev, The volume of a trirectangular hyperbolic tetrahedron // Siberian Electronic Mathematical Reports, 2023, V. 20, No. 1, P. 275–284.
Bio: Professor Nikolay Abrosimov is a professor at the Department of MechanicsMathmatics of Novosibirsk State University. He received a Candidate of Sciences in physics and mathematics in 2009 from the Sobolev Institute of Mathematics. His research interests are hyperbolic geometry, volumes of nonEuclidean polytopes, geometry and topology of threedimensional manifolds, orbifolds, knots and links. He has more than 25 research publications. He is a chairman of the Council of Scientific Youth of the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences.
Volumes of generalized hyperbolic polyhedra and hyperbolic links
Speaker: Andrei Vesnin (Sobolev Institute of Mathematics of RAS)
Time: August 20, 2023 09:3010:30
Location: 正新楼313室
Abstract: A polyhedron in a threedimensional hyperbolic space is said to be generalized if finite, ideal and truncated vertices are admitted. In virtue of Belletti's theorem (2021) the exact upper bound for volumes of generalized hyperbolic polyhedra with the same onedimensional skeleton G is equal to the volume of an ideal rightangled hyperbolic polyhedron whose onedimensional skeleton is the medial graph for G. We will present the upper bounds for the volume of an arbitrary generalized hyperbolic polyhedron, where the bonds linearly depend on the number of edges. Moreover, it is shown that the bounds can be improved if the polyhedron has triangular faces and trivalent vertices. As an application there are obtained new upper bounds for the volume of the complement to the hyperbolic link having more than eight twists in a diagram. The results under discussion are based on the preprint arXiv:2307.04543 (https://arxiv.org/abs/2307.04543).
Bio: Professor Andrei Vesnin is head of the Laboratory of Applied Analysis, Sobolev Institute of Mathematics and a professor of Geometry and Topology, Novosibirsk State University. He received a Candidate of Sciences in physics and mathematics in 1991 from the Sobolev Institute of Mathematics for the thesis “Discrete groups of reflections and threedimensional manifolds”, and a Doctor of Sciences in physics in mathematics in 2005 for the thesis “Volumes and isometries of threedimensional hyperbolic manifolds and orbifolds”.
Professor Vesnin's research interests include lowdimensional topology, knot theory, hyperbolic geometry, combinatorial group theory, graph theory and applications. In 2008, Prof. Vesnin was elected as corresponding member of the Russian Academy of Sciences. He is a member of the editorial board of the journal "International Journal of Mathematics and Computer Science", and doctoral dissertation council at the Institute of Mathematics SB RAS.
YangBaxter equation, RotaBaxter operators and corresponding algebraic systems
Speaker：Valeriy Bardakov （Tomsk State University）
Time：2023年6月28日 14:3015:30
Location：吉林大学数学楼3楼第5研讨室
Abstract: YangBaxter equation is a famous equation in mathematical physics, knot theory and braid theory. There are different generalization of this equation. In particular, tetrahedron equation and nsimplex equation. To describe solutions of these equations where introduced different algebraic systems: rack, quandle, skew brace and some other. The YangBaxter equation connects with RotaBaxter operator on some algeras and groups. Im this talk we will speak on this things and connections between them.
Bio: Valeriy Bardakov is from Tomsk State University. He is a professor of department of algebra and mathematical logic, Faculty of MechanicMathematics, Tomsk State University. His research interests are group theory, knot theory, braid group, automorphism group, symmetric group, PDE, multidimensional inverse problem, evolution equations and integral geometry. He is an author of more than 100 publications.
Since 1995, he has been running the algebraic seminar, "Evariste Galois", at NSU. Since 2000, together with A. Yu. Vesnin, he has been teaching a special course "Algebraic Methods in Knot Theory" at Novosibirsk State University. In 1993, he won the prize M. I. Kargapolov for young mathematicians for solving problems of the Kourovskaya Notebook.
Simplicial structure on pure singular braid groups of camomile type
Speaker：Tatiana Kozlovskaia （Tomsk State University）
Time：2023年6月28日 13:3014:30
Location：吉林大学数学楼3楼第5研讨室
Abstract: In my talk we recall some definitions from Knot Theory, Braid Theory and the construction of J. Wu and F. Cohen which connects braid groups and homotopy groups of 2sphere. In more detail we discuss singular braid groups and its subgroup of pure singular braid group. We describe presentation of these groups and linear representation.
Bio: Tatiana Kozlovskaia is from Scientific and Educational Mathematical Center of Tomsk State University. She is an associated professor of Department of Geometry, Faculty of Mechanicmathematics, Tomsk State University. Her research interests are 3dimensional topology, theory of 3manifolds, lowdimensional geometry, Lens spaces, and Fundamental polyhedra.
Contact geometry via homogeneous symplectic geometry with applications
Speaker：Katarzyna Grabowska （University of Warsaw, Department of Physics）
Time：2023年5月24日 18:0020:00
Meeting ID：ZOOM Id：904 645 6677，Password：2023
会议链接：
https://us02web.zoom.us/j/9046456677?pwd=UHErd3RJVzFsNzNnczFZYm9uYlV6QT09
Abstract: During the talk she will present the novel approach to contact geometry according to which contact structures are not `odddimensional generalizations’ of symplectic geometry but rather particular examples of symplectic geometry, namely homogeneous symplectic principal bundles (with an action of the multiplicative group of nonzero reals). In this setting we are able to construct contact Hamiltonian vector fields even if the global contact form does not exist on the contact manifold in question. The homogeneous symplectic language is also suitable for contact HamiltonJacobi theory and contact reductions.
Bio: Katarzyna Grabowska works in the Department of Mathematical Methods in Physics at the Faculty of Physics. She is interested in differential geometric methods in physics and differential geometry in general.
Topological Ktheory of discrete groups
Speaker：Bailing Wang （The Australian National University）
Time：2023年5月19日 10:3011:30
Meeting ID：腾讯会议：516539518
Abstract: In the 1980’s motivate by the AtiyahSinger index formula, Baum and Connes constructed a topological Ktheory of a discrete group $\Gamma$, together with an assembly map $\mu$ from this mysterious group to the Ktheory group of the reduced C^∗ algebra of $\Gamma$. They conjectured that this assembly map is an isomorphism. The validity of this conjecture implies Novikov conjecture, GromovLawsonRosenberg conjecture and KadisonKaplansky conjecture.
The mathematical details of this construction and the welldefinedness of the assembly map were somewhat missing in their original paper. I will briefly explain some of my earlier work with Paulo Carrillo Rouse on filling up these details, and some recent work with Paulo Carrillo Rouse and Hang Wang on an assembly map to periodic cyclic homology and the ChernConnes pairing formula for any discrete group.
Bio: 王百灵，澳大利亚国立大学教授。1998 年 4月毕业于澳大利亚阿德莱德大学并获得博士学位。毕业先后在德国波恩马普所，法国高等科学研究所， 苏黎士大学做博士后和访问学者。2005年至今在澳大利亚国立大学工作。主要研究规范场理论在低维拓扑中的拓扑不变量、twisted K－同调和twisted指标理论、Gromov－Witten模空间和哈密尔顿Gromov－Witten模空间的K理论等领域。
LIE GROUPOIDS IN INFORMATION GEOMETRY
Speaker：Janusz Grabowski （Polish Academy of Sciences）
Time：2023年5月10日 15:5016: 50
Meeting ID：ZOOM Id：904 645 6677，Password：2023
会议链接：
https://us02web.zoom.us/j/9046456677?pwd=UHErd3RJVzFsNzNnczFZYm9uYlV6QT09
Abstract: After a general introduction to the information geometry, I will show that a natural general setting for statistical and information geometry is the one provided by Lie groupoids and Lie algebroids. The contrast functions are defined on Lie groupoids and give rise to a twoform and a threeform on the corresponding Lie algebroid. If the twoform is nondegenerate, it defines a pseudoRiemannian metric on the Lie algebroid and a family of Lie algebroid torsionfree connections, including the LeviCivita connection of the metric. In this framework, the standard twopoint contrast functions are understood as functions on the pair groupoid MxM and generate a standard (pseudo)Riemannian metrics on M, and families of affine connections on the Lie algebroid TM.
Bio: Professor Janusz Grabowski is the Head of the Department of Mathematical Physics and Differential Geometry in the Institute of Mathematics, Polish Academy of Sciences. His main interests are differential geometry and mathematical physics. As an author of about 140 scientific papers, he published fundamental results on Lie algebras of vector fields, diffeomorhism groups, Lie systems, Poisson and Jacobi manifolds, Lie groupoids and algebroids, Lagrangian and Hamiltonian mechanics (including mechanics on contact manifolds), supergeometry, geometry of quantum states and entanglement, etc. His personal page is https://www.impan.pl/~jagrab/.
Regular subgroups, skew braces, gamma functions and Rota–Baxter operators
Speaker：Andrea Caranti （University of Trento, Italy）
Time：2023年4月19日 20:0022:00
Meeting ID：ZOOM Id：904 645 6677，Password：2023
会议链接：
https://us02web.zoom.us/j/9046456677?pwd=UHErd3RJVzFsNzNnczFZYm9uYlV6QT09
Abstract: Skew braces, a novel algebraic structure introduced only in 2015, have already spawned a sizeable literature. The skew braces with a given additive group structure correspond to the regular subgroups of the permutational holomorph of such a group. These regular subgroups can in turn be described in terms of certain socalled gamma functions from the group to its automorphism group, which are characterised by a functional equation. We will show how gamma functions can be used in studying skew braces, underlining in particular their relationship to RotaBaxter operators.
Bio: Andrea Caranti is a Senior Professor of Algebra at the University of Trento, Italy. He has worked mainly in group theory (nilpotent groups, automorphisms, applications to cryptography) and on graded, modular Lie algebras. His recent work concerns grouptheoretical aspects of skew braces.
On pseudoEuclidean Lie algebras whose LeviCivita product is left Leibniz
Speaker：Said Benayadi （University of LorraineMetz）
Time：2023年3月30日 20:0021:00
Meeting ID：ZOOM Id：904 645 6677，Password：2023
会议链接：
https://us02web.zoom.us/j/9046456677?pwd=UHErd3RJVzFsNzNnczFZYm9uYlV6QT09
Abstract: We study a class of Lie algebras which contains the class of quadratic Lie algebras and the class of Milnor Lie algebras, namely, Lie algebras endowed a pseudoEuclidean metric such its Levi Civita product is left Leibniz. We call them LeviCivita left Leibniz Lie algebras LCLL for short. We show that a Lie group (G, h) endowed with a left invariant pseudoRiemannian such that the corresponding Lie algebra is LCLL is complete and locally symmetric. Moreover, we prove that any Euclidean LCLL Lie algebra is the product of quadratic a Lie algebra and a flat Euclidean Lie algebra. We develop an adapted version of the process of double extension to construct LCLL Lie algebras. We show that Lorentzian or flat LCLL Lie algebras can be obtained by this process.
Bio: Said Benayadi is a professor in University of LorraineMetz. His research interest is nonassociative algebras.
Singular foliations and Qmanifolds
Speaker：Camille LaurentGengoux （Université de Lorraine, Metz）
Time：2023年3月22日 16:0017: 00
Meeting ID：ZOOM ID：904 645 6677，Password：2023
会议链接：
https://us02web.zoom.us/j/9046456677?pwd=UHErd3RJVzFsNzNnczFZYm9uYlV6QT09
Abstract: In this talk, we will explain how a Qmanifold (equivalently, a Lie infinity algebroid) can be associated to a singular foliation, and how this Qmanifold helps in studing the geometry of the latter. Joint works with Sylvain Lavau, Ruben Louis, Leonid Ryvkin, Thomas Strobl.
Bio: Camille LaurentGengoux is a professor in Université de Lorraine, Metz. He mainly studies Poisson geometry and related structures. He authored more than 40 scientific articles in J. Eur. Math. Soc., Math. Ann., Adv. Math., Int. Math. Res. Not. and other journals.
On a certain family of vertex algebras associated with vertex algebroids
Speaker：Haisheng Li （Rutgers UniversityCamden）
Time：2023年3月9日 09:0010:00
Meeting ID：ZOOM Id：904 645 6677，Password：2023
会议链接：
https://us02web.zoom.us/j/9046456677?pwd=UHErd3RJVzFsNzNnczFZYm9uYlV6QT09
Abstract: This talk is about a family of vertex algebras associated with vertex algebroids, constructed by Gorbounov, Malikov, and Schechtman. As the main result, we classify all the (graded) simple modules for such vertex algebras and we show that the equivalence classes of graded simple modules onetoone correspond to the equivalence classes of simple modules for the Lie algebroids associated with the vertex algebroids. To achieve our goal, we construct and exploit a Lie algebra from a given vertex algebroid. This talk is based on a joint work with Gaywalee Yamskulna.
Bio: Haisheng Li is a professor of Rutgers UniversityCamden. His main research is on vertex operator algebras and quantum vertex algebras. Among the main results are conceptual constructions of vertex algebras and their modules, twisted modules; A theory of quasi modules; A theory of (weak) quantum vertex algebras and φcoordinated modules; A conceptual association of double Yangians and quantum affine algebras with quantum vertex algebras. He published more than 100 articles in Duke Math. J., Com. Math. Phys., Adv. Math., Tans. AMS and other Internationally renowned journals.
On local integration of Lie brackets
Speaker：María Amelia Salazar Pinzón （Universidade Federal Fluminense）
Time：2023年2月16日 21:0022:00
Meeting ID：ZOOM Id：904 645 6677，Password：2023
会议链接：
https://us02web.zoom.us/j/9046456677?pwd=UHErd3RJVzFsNzNnczFZYm9uYlV6QT09
Abstract: The foundation of Lie theory is Lie's three theorems that provide a construction of the Lie algebra associated to any Lie group; the converses of Lie's theorems provide an integration, i.e. a mechanism for constructing a Lie group out of a Lie algebra. The Lie theory for groupoids and algebroids has many analogous results to those for Lie groups and Lie algebras,however, it differs in important respects: one of these aspects is that there are Lie algebroids which do not admit any integration by a Lie groupoid. In joint work with Cabrera and Marcut, we showed that the nonintegrability issue can be overcome by considering local Lie groupoids instead. In this talk I will explain a construction of a local Lie groupoid integrating a given Lie algebroid and I will point out the similarities with the classical theory for Lie groups and Lie algebras.
Bio: María Amelia is a professor at Departamento de Matemática Aplicada (GMA) of the Universidade Federal Fluminense (UFF), Brazil.The main research interests are Lie groupoids, Lie algebroids, Lie pseudogroups, geometry of PDE's, Poisson geometry, contact and symplectic geometry.
Local and 2local derivations and automorphisms of Octonian algebras
Speaker：Shavkat Ayupov (Institute of Mathematics, Uzbekistan Academy of Sciences)
Time：2023年2月9日 16:0017:00
Meeting ID：ZOOM Id：904 645 6677，Password：2023
会议链接：
https://us02web.zoom.us/j/9046456677?pwd=UHErd3RJVzFsNzNnczFZYm9uYlV6QT09
Abstract:
The talk is devoted to description of local and 2local derivations (respectively, automorphisms) on octonian algebras. We shall give a general form of local derivations on the octonion algebra O(F) over a field F with zero characteristic. This description implies that the space of all local derivations on O(F) when equipped with Lie bracket is isomorphic to the Lie algebra so7 O(F) of all real skewsymmetric 7 × 7matrices over F. At the same time the Lie algebra of all derivations are isomorphic to the exceptional Lie algebra g_{2}(F). It follows that the octonion algebra O(F) and Malcev algebra M7(F) over the field F are simple non associative algebras which admit pure local derivations, that is, local derivations which are not derivation.
Further we consider 2local derivations on the octonion algebra O(F) over an algebraically closed field F and prove that every 2local derivation on O(F) is a derivation. But for the field R of real numbers 2local derivations on the octonian algebra O(R) form a Lie algebra which is essentially larger than the Lie algebra g_{2}(R) of derivations. we apply these results to problems for the simple 7dimensional Malcev algebra. We shall give a general form of local automorphisms on the octonion algebra O(F). This description implies that the group of all local automorphisms on O(F) is isomorphic to the group O_{7}(F) of all orthogonal 7 × 7matrices over F, and it is essentially larger than the group of all automorphisms.
We also consider 2local automorphisms on the octonion algebra O(F) over an algebraically closed field F and prove that every 2local automorphism on O(F) is an automorphism. At the same time the group of 2local automorphisms of O(R) is larger than the group of automorphisms of O(R). As a corollary we obtain descriptions of local and 2local automorphisms of seven dimensional simple Malcev algebra.
Bio: Shavkat Ayupov is the Director of V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences. His field of scientific interest include Theory of Operator Algebras and Quantum Probability, Structure theory of Nonassociative algebras (Jordan, Lie, Leibniz, etc.). He is the authors of several monograph devoted to Real and Jordan structures on Operator Algebras, also to the structure theory of Leibniz algebras. Sh. Ayupov is a Member of Uzbekistan Academy of Sciences (since 1995), Fellow of TWAS (The World Academy of Sciences) (since 2003), Senior Associate of ICTP (International Centre for Theoretical Physics) (2008 – 2013), Guest Professor of Sichuan University (Chengdu, China) (20152021). He is the Managing Editor of Uzbek Mathematical Journal and editor of “Advances in Operator Theory”.
In 2017, he was awarded the State Prize of the first degree in the field of Science and Technology of the Republic of Uzbekistan.
Arborescent KoszulTate resolutions and BFV for singular coisotropic reductions
Speaker：Thomas Strobl (University of Lyon)
Time：2023年1月12日 20:0021:00
Meeting ID：ZOOM Id：904 645 6677，Password：2023
会议链接：
https://us02web.zoom.us/j/9046456677?pwd=UHErd3RJVzFsNzNnczFZYm9uYlV6QT09
Abstract：
Bio：Thomas Strobl is a professor in the mathematics department at the University of Lyon. His work as a mathematical physicist is mainly concerned with geometric and algebraic aspects of sigma models and gauge theories. In 1993, during his PhD thesis and together with P. Schaller, he discovered the Poisson Sigma Model; it was used later by M. Kontsevich to obtain his famous quantization formula. In 2015 he and A. Kotov introduced a generalisation of YangMills gauge theories to the Lie algebroid setting. In total, in his career he authored more than 60 scientific articles.
Subalgebras of free algebras
Speaker：Vladimir Dotsenko （University of Strasbourg）
Time：2023年1月5日 16:0017:00
Meeting ID：ZOOM Id：904 645 6677，Password：2023
会议链接：
https://us02web.zoom.us/j/9046456677?pwd=UHErd3RJVzFsNzNnczFZYm9uYlV6QT09
Abstract：A classical result going back to works of Shirshov and Witt in 1950s states that every subalgebra of the free Lie algebra is free. Understanding what makes a variety of algebras satisfy this property has been an important open question in ring theory, recorded, for instance, in the Dniester Notebook. I shall talk about a recent work with Ualbai Umirbaev in which we developed a method that allowed us to exhibit infinitely many varieties of algebras (with one binary operation) satisfying this property; prior to our work, only six such varieties had been known. One surprising consequence of our work is that for the variety of all rightsymmetric algebras subalgebras of free algebras are free.
Bio：Vladimir Dotsenko is a professor at the University of Strasbourg, France. His work applies ideas of category theory to concrete questions of algebra, combinatorics, geometry and topology.
On the subspaces and quotients of C(K) spaces with few operators
Speaker：ALIRIO GOMEZ GOMEZ (Institute of Science and Technology of the Federal University of São Paulo) (ICTUNIFESP)
Time：2022年12月15日 20:0021:00
Meeting ID：Zoom ID：862 062 0549，Password：2022
会议链接：
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract：
Bio：At this moment he is a postdoc student at Federal University of São Paulo, where he is studying Lipschitz free Banach spaces and their applications. Also, he has continued working on Banach spaces C(K) with few operators which was the topic of his doctoral dissertation. As a result, a manuscript on the subspaces of linear operators on C(K) contained in the set of not weak multiplier operators is being completed in collaboration with R. Fajardo and L. Pellegrini. Before he joints UNIFESP, he pursued his PhD in mathematics. In his PhD thesis they found some topological conditions on a compact K, related to the property of C(K) having few operators. They also proved that there exists an indecomposable C(K) that has some not weak multiplier operators. Moreover, assuming the Diamond Principle, they constructed a compact nonweakly Koszmider Space K, which has no trivial retractions. In the next couple of months he will move to Rio de Janeiro where he will be a Professor at Rio de Janeiro State University.
Stokes phenomenon and representation of quantum groups
Speaker：Xiaomeng Xu (Peking University)
Time：2022年12月8日 15:3016:30
Meeting ID：
Zoom ID：862 062 0549，Password：2022
会议链接：
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract：Stokes phenomenon states that the asymptotic behavior of functions can differ in different regions of the complex plane, and that these differences can be described in a quantitative way. The quantities, the socalled Stokes matrices, have played important roles in many subjects. This talk gives an introduction to the Stokes phenomeon of a meromorphic linear system of ordinary differential equations，and then discusses various unsolved analysis problems, with a relation to the representation theory of quantum groups.
Bio：徐晓濛，北京大学助理教授，2016年获日内瓦大学博士学位，主要研究方向是表示论、辛几何、奇点理论及其在数学物理中的应用。目前在Adv. Math., Comm. Math. Phys., Int. Math. Res. Not. 等数学期刊发表多篇论文。
Some constructions from graded geometry
Speaker：Vladimir Salnikov (CNRS / La Rochelle University)
Time：2022年12月1日 15:3016:30
Meeting ID：Zoom ID：862 062 0549，Password：2022
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract：In this talk I introduce some natural constructions from the "graded world", paying particular attention to the differences between N and Z graded manifolds. I will start by the construction of the sheaf of functions on graded manifolds and describe its structure. The intrinsic properties of this functional space are conveniently given using the language of filtrations, allowing to formulate the analog of Batchelor’s theorem. Afterwards I will briefly introduce graded Hopf algebras and HarishChandra pairs, which in turn provide the result of equivalence of categories between graded Lie groups and algebras. These constructions are then used to solve the integration problem of differential graded Lie algebras to differential graded Lie groups. Time permitting, I will also say a few words on canonical forms of differential graded manifolds.
Bio：Vladimir Salnikov is a researcher at CNRS (National Centre for Scientific Research), La Rochelle University, France. His scientific interests are graded and generalized geometry, dynamical systems, applications to mechanics and theoretical physics.
Racks, Leibniz algebras and rack bialgebras
Speaker：Friedrich Wagemann (University of Nantes)
Time：2022年11月29日12月2日
Meeting ID：Zoom ID：862 062 0549，Password：2022
Abstract：Groups, Lie algebras and associative bialgebras are linked by various functors which are important in Lie theory. We argue that this triad may be generalized to Racks, Leibniz algebras, rack bialgebras, which enjoy roughly the same links. In this minicourse, we will mainly discuss the cohomology of these structures.
Date of Lecture 
Name (Title) of Lecture 
Beijing Time 
November29, 2022 
Groups,Lie algebras and associative bialgebras 
20:0021:00 
November29, 2022 
Racks, Leibniz algebras and rack bialgebras 
21:0022:00 
November30, 2022 
Cohomology of Racks 
20:0021:00 
November30, 2022 
Periodicity in algebraic Ktheory 
21:0022:00 
December1, 2022 
Cohomology of Leibniz algebras 
20:0021:00 
December1, 2022 
Cohomology of nilpotent Leibniz algebras 
21:0022:00 
December2, 2022 
Deformation cohomology of rack bialgebras 
20:0021:00 
December2, 2022 
Deformation cohomology of rack bialgebras vs cohomology of Leibniz algebras 
21:0022:00 
Bio：Friedrich Wagemann, is a Professor from University of Nantes, France. He mainly studies Lie Theory and Mathematical Physics. He has published more than 40 highlevel academic papers in Comm. Math. Phys., Adv. Math., Trans. Amer. Math, Soc., Pro. Lond. Math. Soc., IMRN and other journals.
Quasilocal mass and geometry of scalar curvature
Speaker：Yuguang Shi (Peking Universtiy)
Time：2022年11月25日 10:3011:30
Meeting ID：腾讯会议：520112012
Abstract：Let (Σ^(n1),γ) be an (n1)dimensional orientable Riemannian manifold, H be a positive function on Σ^(n1), Gromov’s asked under what conditions γ is induced by a Riemannian metric g with nonnegative scalar curvature, for example, defined on Ω^n, and H is the mean curvature of Σ in (Ω^n,g) with respect to the outward unit normal vector? By the recent result due to P. Miao we know such H cannot be too large, so the next natural question is what is “optimal” H so that such a fillin for the triple (Σ^(n1),γ,H) exits? It turns out that the problem has deep relation with positive mass theorem, in this talk I will talk about some known results relate to this topic. My talk is based on my joint works with Dr. Wang Wenlong, Dr.Wei Guodong，Dr. Zhu Jintian, Dr.Liu Peng, Dr. Hu Yuhao.
Bio：史宇光，1996年在中科院数学研究所获博士学位，1997年至1999年分别于香港中文大学，北京大学数学科学学院从事博士后研究，后留北大工作。曾获得国家杰出青年基金项目资助，当选长江特聘教授，入选第二批国家“万人计划”科技创新领军人才。于2010年，获第十一届中国青年科技奖；2011年，获理论物理国际中心（ICTP）Ramanujan奖；2020年，获教育部高等学校科学研究自然科学奖一等奖。
Local derivations and automorphisms on solvable Lie algebras of maximal rank
Speaker：Bakhrom Omirov (National University of Uzbekistan)
Time：2022年11月18日 10:3011:30
Meeting ID：ZOOM ID：862 062 0549，Code：2022
会议链接：
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract：The present talk is devoted to the description of local derivations and automorphisms on solvable Lie algebras of maximal rank. First, we present the general form of an automorphism on solvable Lie algebra of maximal rank. Namely, any automorphism can be represented as a composition of inner, diagonal and graph automorphisms. We show that all local derivations and all local automorphisms of solvable Lie algebra of maximal rank are global, while there are examples of solvable Lie algebras of nonmaximum rank with different behavior of local derivations and local automorphisms. We also apply the main results to the descriptions of local derivations and local automorphisms on standard Borel subalgebras of complex simple Lie algebras.
Bio：Bakhrom Omirov is a professor at the National University of Uzbekistan. His research focused on nonassociative algebras and superalgebras. In particular, he is one of the authors of the monograph devoted to the structure theory of Leibniz algebras. Bakhrom Omirov is a member of The World Academy of Sciences, which includes 66 countries), as well as Uzbek and American Societies. He is a winner of several prestigious fellowships (Fulbright, USA; INTAS, Belgium).
On the first cohomology group of Murrayvon Neumann algebras
Speaker：Karimbergen Kudaybergenov (V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences)
Time：2022年11月18日 15:3016:30
Meeting ID：ZOOM ID：862 062 0549，Code：2022
会议链接：
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract：This talk presents a full resolution of the problem stated by Ayupov in 2000 and partly restated in 2014 by Kadison and Liu. We explain a background of the Ayupov–Kadison–Liu Problem and its connection with general derivation theory in operator algebras starting with fundamental results due to Kaplansky, Kadison, Sakai and others. We shall cite and brief explain major results concerning derivations on algebras of unbounded operators and list results concerning some special cases of the problem. Finally, the main result yielding the full resolution will be stated.
Bio：Karimbergen Kudaybergenov is a head at the Karakalpak branch of V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences. His research focused on operator algebras and mappings on nonassociative algebras. Karimbergen Kudaybergenov is an influential expert in the studies of derivations of unbounded operator algebras, who is also an exceptionally prolific author publishing his results in top internationally recognized journals. The highest quality of his research contributions has been recognized in Uzbekistan. In 2017, he was awarded the State Prize of the first degree in the field of Science and Technology of the Republic of Uzbekistan. Further, in 2017, he was awarded an Honored Scientist of the Republic of Karakalpakstan.
Equilibrium programming: background and some new concepts
Speaker：Boris Budak （Moscow State University）
Time：2022年11月17日 15:4516:45,
Meeting ID：ZOOM ID：862 062 0549，Code：2022
会议链接：
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract：Equilibrium programming is a broad area of mathematics that studies mathematical models of numerous phenomena in natural sciences and economics. A typical situation is when exact values of functional Φ(v,w) are not available when finding the numerical solution to the equilibrium programming problem and we have only their approximations. It is known that numerical models do not always work correctly in that situation, and different types of regularization must be applied. One of the bestknown of these is Tikhonov’s regularization, which is usually used in processing approximate data. Some classic and new concepts of regularization will be discussed, a new regularized shooting model based on Tikhonov regularization for solving problems of equilibrium programming with inexact data will be given as an example.
Bio：Boris Budak is an associated professor of Faculty of Computational Mathematics and Cybernetics, Moscow State University. His Main Scientific Interests and Results including:
1. Extremal problems with disturbed data, optimal control, stabilization and regularization.
2. Developed and investigated a family of continuous methods for equilibrium programming problems solving, developed regularized analogues of these methods for the situation, when initial data is disturbed.
3. Created a new socalled “shooting” method for equilibrium programming problems solving, developed regularized analogue of it.
4. Solved some problems dedicated to a search of an operator with minimal norm, that guarantees a given solution of a linear operator equation in Hilbert spaces.
Complex cobordisms, the universal formal group, and theta divisors
Speaker：Victor Matveevich Buchstaber (Steklov Mathematical Institute, Russian Academy of Sciences)
Time：2022年11月11日 15:3016:30
Meeting ID：ZOOM ID：862 062 0549，Code：2022
会议链接：
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract: The talk is devoted to fundamental connections between algebraic topology, the formal groups theory and algebraic geometry.
The focus will be on the result of V.M. Buchstaber and A.P. Veselov, 2020. According to this result the exponent of the universal onedimensional formal group is given by a series f(t) with the coefficient at t^{n+1}/ (n+1)! which is equal to the complex cobordism class of the theta divisor of a general (n+1)dimensional abelian variety. We will discuss the applications of this result to wellknown problems of algebraic topology and algebraic geometry, including the still open MilnorHirzebruch problem on the Chern numbers of irreducible smooth algebraic varieties.
The talk is designed for a wide audience, all the necessary concepts will be introduced.
Bio: Prof. Victor Matveevich Buchstaber is an expert in algebraic topology, geometric combinatorics, mathematical physics, founder of a large scientific school in topology and its applications, corresponding member of the Russian Academy of Sciences, chief scientific researcher of the Moscow Mathematical V.A.Steklov Institute, professor of the Moscow State M.V. Lomonosov University, Vice President of the Moscow Mathematical Society.
Conservative algebras
Speaker：Ivan Kaygorodov （University of Beira Interior）
Time：2022年11月04日 15:3016:30
Meeting ID：ZOOM ID：862 062 0549，Code：2022
会议链接：
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract: The class of conservative algebras was introduced in 1972 by I. Kantor. Roughly speaking, it is a class of algebras satisfying a "quasiidentity'' of degree 4. The class of conservative algebras includes many important varieties of algebras, such as associative algebras, Lie algebras, Leibniz algebras, Zinbiel algebras, Jordan algebras, etc. Conservative algebras and superalgebras have some similar properties to many wellknown varieties of algebras. For example, they admit the TitsKoecherKantor construction (TKK construction); each conservative algebra (and superalgebra) could be embedded in a suitable universal conservative algebra (or superalgebra). We will talk about some old and new results from this topic.
Bio: Ivan Kaygorodov got his Ph.D. in 2010 at the Sobolev Institute of Mathematics (Russia). He has worked as a postdoctoral researcher at the University of Sao Paulo (Brazil) and as an assistant professor at the Federal University of ABC (Brazil) for 10 years. Now he is a research fellow at the University of Beira Interior (Covilhã, Portugal). He is the EditorinChief of Communications in Mathematics. His main area of research interest is in nonassociative algebras.
Weak Leibniz algebras and transposed Poisson algebras
Speaker：Askar Jumadildayev (KazakhBritish Technical University）
Time：2022年10月28日 14:0015:00
Meeting ID：ZOOM ID：862 062 0549，Code：2022
会议链接：
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract: Weak Leibniz algebras are defined by the following identities: $[a,b]c=2(a(bc)b(ac))$ and $a[b,c]=2((ab)c(ac)b).$ Any twosided Leibniz algebra, in particular any Lie algebra is weak Leibniz. We show that polarization of any weak Leibniz algebra is transposed Poisson and conversely, depolarization of any transposed Poisson algebra is weak Leibniz. Well known that any simple Leibniz algebra is Lie. We construct simple weak Leibniz algebras that are not Lie.
Bio: Askar Jumadildayev is a professor of KazakhBritish Technical University. His research interests concern cohomologies and deformations of Lie algebras, Ncommutators of vector fields, identities of nonassociative algebras and operads theory.
SUbordism: geometric representatives, operations, multiplications and projections
Speaker：Panov Taras (Moscow State University)
Time：2022年10月21日 15:0016:00
Meeting ID：ZOOM ID：862 062 0549，Code：2022
会议链接：
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract: The development of algebraic topology in the 1960s culminated in the description of the special unitary bordism ring. Most leading topologists of the time contributed to this result, which combined the classical geometric methods of ConnerFloyd, Wall and Stong with the AdamsNovikov spectral sequence and formal group law techniques that emerged after the fundamental 1967 work of Novikov.
Thanks to toric topology, a new geometric approach to calculations with SUbordism has emerged, which is based on representing generators of the SUbordism ring and other important SUbordism classes by quasitoric manifolds and CalabiYau hypersurfaces in toric varieties.
We shall also discuss more specific topics related to SUbordism. Namely we show that SUlinear operations in complex cobordism are generated by the wellknown geometrical operations $\partial_i$. For the theory $W$ of $c_1$spherical bordism, we describe SUlinear multiplications on W and projections $MU \to W$. We also analyse complex orientations on $W$ and prove results on the snumbers of the coefficients of the corresponding formal group laws.
The talk is based on joint work with Zhi Lu, Ivan Limonchenko and Georgy Chernykh.
Bio: Panov Taras，Professor, Faculty of Mathematics and Mechanics, Moscow State University; Moscow Mathematical Society prize (2004); Shuvalov Prize of Moscow University (2010).
Personal Web Page: http://higeom.math.msu.su/people/taras/english.html.
Properties of polynomial maps and twodimensional Jacobian conjecture
Speaker：Yucai Su （Tongji University）
Time：2022年10月14日 14:3015:30 Beijing time
Meeting ID：ZOOM ID：862 062 0549，Code：2022
会议链接：
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract: For any two polynomials on two variables with a nonzero Jacobian determinant, there corresponds a polynomial map known as a Keller map. In this talk, the speaker will report 3 properties of Keller maps, which are used to give a proof of the twodimensional Jacobian conjecture in the speaker’s paper entitled ``a proof of 2dimensional Jacobian conjecture'' at arXiv:1603.01867.
Bio: Yucai Su is a professor at Tongji University and Jimei University. He has successively worked as a visiting scholar and postdoctoral researcher at Queen Mary and Westfield College, the University of London, Concordia University, and the University of Quebec at Montreal for 7 years. His main research interests include Lie algebras, representation theory and Jacobian problem. In particular, he has studied the Jacobian Conjecture for eighteen years. He is an editor of Algebra Colloquium and Journal of Mathematical Study, and published over 100 papers in Adv. Math., J. Eur. Math. Soc., Proc. London Math. Soc., Comm. Math. Phys., Math. Z., Israel J. Math., etc. Recently, using the local bijectivity of Keller maps, he solved the 2dimensional Jacobian Conjecture.
FROM OPERADS TO OPERADIC CATEGORIES
Speaker：Michael Batanin （Institute of Mathematics of Czech Academy of Science, Charles University, Prague）
Time：2022年09月30日 16:3017:30
Meeting ID：ZOOM ID：862 062 0549，Code：2022
会议链接：
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract: Operads were introduced at the end of 1960s by Boardman, Vogt and P.May as spaces parametrising multivariable operations and their substitutions. In the 1990's however, it was realised that there are other interesting types of operads such as cyclic and modular operads of Getzler and Kapranov (motivated by TQFT development) and globular noperads of Batanin parametrising higher categorical compositional structures. In 2015 Batanin and Markl introduced operadic categories in order to develop a consistent theory of operadic like structures. In my talk I explain what operadic category and associated category of operads are and why this is a very rich and useful new algebraic concept.
Bio: The speaker graduated from Novosibisk State University in 1983. He is currently a Senior Researcher at the Institute of Mathematics of Czech Republic, and a Professor of Charles University in Prague. He is specialising in Algebraic Topology, Category Theory, Operads and related topics.
International Frontiers of Mathematics
Zoom ID: 862 062 0549 Password: 2022
孤立波：18341984
Speaker：张大军 上海大学
Time：2022年09月23日 10:3011:30
Meeting ID：腾讯会议：309266962
腾讯会议链接：https://meeting.tencent.com/dm/jx2ianwNTLKT
Abstract: 这是一个关于“孤立波”的历史与发展的科普报告。1834年 John Scott Russell首次发现孤立波，1895年Korteweg和de Vries (KdV) 利用KdV方程描述了孤立波现象， 1965年 Kruskal 和 Zabusky在研究FermiPastaUlam问题时发现并命名了“soliton” (孤立子), 两年以后GardnerGreeneKruskalMiura 建立了反散射方法(Inverse Scattering Transform), 成为现代可积理论的起点。报告将回顾孤立波与可积系统在前150年(18341984)的历史，回顾期间(特别是19681984)出现的重要的可积模型以及重要的理论与方法进展。
Bio: 张大军，上海大学数学系教授，博士生导师。主要从事离散可积系统与数学物理的研究，包括离散可积系统的直接方法、多维相容性的应用、空间离散下的可积结构与连续对应等。曾访问Turku大学、Leeds大学、剑桥牛顿数学研究所、Sydney大学等学术机构。先后主持国家自然科学基金面上项目5项。目前担任离散可积系统国际系列会议SIDE (Symmetries and Integrability of Difference Equations)指导委员会委员(2012)和国际期刊Journal of Physics A编委(2020)。
Coarse geometry and operator algebras : a minicourse
Speaker：Yeong Chyuan Chung 博士后 Leiden University
Meeting ID：腾讯会议：86921186000，密码：3721
腾讯会议链接：https://meeting.tencent.com/dm/x708itdk0Eq1
Abstract: Coarse geometry involves studying metric spaces by looking at them from far away, and it is important in areas of mathematics such as geometric group theory. In recent times, its interaction with operator algebras has also been an active area of research with applications to problems in topology and differential geometry. In this minicourse, we aim to introduce basic notions in coarse geometry and a class of operator algebras known as Roe algebras. Starting from coarse geometry, we will introduce basic definitions such as coarse embeddings and coarse equivalences, then we will introduce some coarse geometric invariants such as asymptotic dimension and property A. Next, we will introduce Banach algebras and C*algebras with examples of these, then we will focus on Roe algebras and how they reflect the coarse geometry of the underlying metric spaces. Finally, we will briefly introduce operator Ktheory and the coarse BaumConnes conjecture involving the Ktheory of Roe algebras.
授课日期 Date of Lecture 
课程名称（讲座题目） Name (Title) of Lecture

授课时间 Duration 
参与人数 Number of Participants 
Sep 19, 2022 
Introduction to coarse geometry: basic definitions and asymptotic dimension 
19:3020:30 
30 
Sep 20, 2022 
Introduction to coarse geometry: property A 
19:3020:30 
30 
Sep 21, 2022 
Banach algebras and C*algebras with examples 
19:3020:30 
30 
Sep 22, 2022 
Roe algebras I 
19:3020:30 
30 
Sep 26, 2022 
Roe algebras II 
19:3020:30 
30 
Sep 27, 2022 
Basic operator Ktheory 
19:3020:30 
30 
Sep 28, 2022 
Ktheory of Roe algebras and the coarse BaumConnes conjecture 
19:3020:30 
30 
Sep 29, 2022 
A quick look at a counterexample to the coarse BaumConnes conjecture 
19:3020:30 
30 
Bio: Yeong Chyuan Chung（钟永权），2017年博士毕业于美国德州农工大学, 主要从事粗几何、L^p算子代数、K理论的研究。 近年来在J. Funct. Anal.，J. Noncommut. Geom.等杂志上发表多篇高水平论文。
Advanced Numerical Methods with Applications
Speaker：Andrey Dorogovtsev professor（Institute of Mathematics，NAS Ukraine）
Meeting ID：Zoom会议 ID：会议号：852 4434 8793，密码：075030
Abstract: This course aims to provide a solid introduction on some advanced numerical methods and its applications. The first part of the course will introduce the definition of local times and Gaussian functionals, then discuss some properties when local times as a Gaussian functionals. And the second part of the course is devoted to introduce Hausdorff measure and dimension, then use the Hausdorff measure and dimension to discuss sefintersections set of Brownian motion. Professor Andrey will give students some time to understand the knowledge and give some small questions about the lecture.
授课日期 Date of Lecture 
课程名称（讲座题目） Name (Title) of Lecture 
授课时间 Duration (Beijing Time) 
参与人数 Number of Participants 
20220919 
Local times and sets of values of random fields 
16:0017:00 
30 
20220921 
Gaussian white noise and functionals from it 
16:0017:00 
30 
20220926 
Local times as a Gaussian functionals 
16:0017:00 
30 
20220928 
Local nondeterminism for Gaussian random fields 
16:0017:00 
30 
20221003 
Hausdorff measure and dimension 
16:0017:00 
30 
20221005 
Haussdorf dimension for sefintersections set of Brownian motion 
16:0017:00 
30 
Bio: Andrey Dorogovtsev教授是乌克兰国家科学院通讯院士，乌克兰国家科学院数学所随机过程理论系主任，主要从事概率论及其相关领域研究，是乌克兰概率论研究方向学术领军人物之一。Andrey Dorogovtsev教授是乌克兰与德国、乌克兰与俄罗斯等国家联合项目的乌方负责人。同时，Andrey Dorogovtsev教授是《Theory of Stochastic Processes》、《Ukraine Mathematical Journal》等杂志的编委。
Noncommutative differential geometry and quantum effects of gravity
Speaker：张晓（中国科学院数学与系统科学研究院）
Time：2022年09月16日 10:3011:30
Meeting ID：腾讯会议 ID：602653169
点击链接入会：https://meeting.tencent.com/dm/7TgVgfHRMj51
Abstract: We provide a rigorous theory of noncommutative metrics and curvatures in frame of deformation quantization. In terms of them, we are able to propose the noncommutative Einstein field equations. We show that the deformation of classical ppwaves are exact solutions of vacuum field equations. We also find that the quantization of spherically symmetric metrics is renormalizable and the deformation of classical Schwarzschild solution is the quantum black hole solution which does not depend on time and can not be evaporated. The talk is based on the early joint works with Chaichian, Tureanu, D. Wang, R.B. Zhang as well as H. Gao recently.
Bio: 张晓，中国科学院数学与系统科学研究院数学研究所研究员，国家杰出青年基金及中科院百人计划获得者。现任广西大学君武学者和广西八桂学者，广西数学研究中心执行主任。从事广义相对论的数学研究，在广义相对论正能量问题及引力量子化的非交换几何理论上作出了系统性的贡献。
Higher algebraic structuresa minicourse
Speaker：Camilo Andres Angulo Santacruz（Universidade Federal Fluminense）
Meeting ID：ZOOM ID：862 062 0549 Password：2022
点击链接入会：
https://zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Course Abstract：“Higher structure” is a term used loosely to refer to a large collection of structures that share a common theme. Suppose a mathematical structure consists of a collection of sets, functions between them, and some equations that the latter shall verify. Think of group structures, for instance, as the sets G, GxG, and the singleton, together with three functions (the multiplication, the unit, and the inverse) that verify the usual axioms of a group, which are equations relating them(!). The common idea behind higher structures is that they roughly are like mathematical structures, but replacing sets by homotopy types, equations by homotopies, and adding higherorder homotopies to enforce coherence.
Higher structures have an intricate history and abound in mathematics. We will focus on three types of higher structures that have algebraic flavor.In what follows we describe the plan of the lectures. We will start by giving a bit of a panoramic perspective on the history and emergence of the higher structures we will consider. After going through some preliminaries, we proceed to study them one by one, starting with the socalled Linfinity algebras, continuing with stacky groupoids, and closing with Lie ngroupoids. In each module, we go through definitions, examples, and main constructions. We conclude by trying and relating these structures among them and by giving an outlook for the directions in which these generalize by touching upon some recent research topics.
Bio：Camilo Andres Angulo Santacruz is a post doctor from Universidade Federal Fluminense, Brazil. He mainly study Poisson geometry and higher structures.
怪波/畸形波简介
Speaker：闫振亚（中科院数学院系统所）
Time：2022年09月09日 10:3011:30
Meeting ID：腾讯会议 ID：737700086
点击链接入会：https://meeting.tencent.com/dm/VWCgdy2stinj
Abstract: 不同于通常的孤子(soliton), 怪波（rogue wave/rogon）拥有巨大的能量，也被称为畸形波、巨波、极端波等。它最早出现在深水海洋中，后来人们发现很多自然科学中也存在怪波现象，如光学、BoseEinstein凝聚态、等离子体物理、大气科学、生物学和金融市场等。从某种意义来说，社会科学中的突发问题也属于怪波范畴。本报告介绍线性和非线性科学问题中怪波的背景、发展和挑战等。另外讨论怪波产生的一些物理机理等。
Bio: 闫振亚，中科院数学院系统所研究员，主要研究可积系统理论、怪波、PT对称、智能数学物理及交叉应用等。2019年获得国家自然科学基金杰出青年基金。
Operators on the universal enveloping algebras and quantisation of the argument shift method
Speaker：Georgy Sharygin（Lomonosov Moscow State University）
Time：2022年09月09日 21:0022:00
Meeting ID：ZOOM ID：862 062 0549 Password：2022
点击链接入会：
https://zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract: Argument shift method is an important and simple method to generate large commutative subalgebras in Poisson algebras, in particular in the algebras of functions on coadjoint representation of a Lie algebra. In the last 20 years a considerable in finding "quantized version" of such algebras was achieved: in the papers of Rybnikov, Molev and others one can find many examples of commutative subalgebras in the universal enveloping algebras of different Lie algebras, that "raise" the subalgebras, obtained by the argument shift method. However these subalgebras are constructed by "quantizing" concrete sets of generators in the "classical" argument shift subalgebras, and no general construction of "shifting" in the universal enveloping algebras is known. In my talk I will discuss a potential "quantum counterpart" of the shift in a particular case of the Lie algebra gl_n. It is based on the use of "quasiderivations" of Ugl_n, introduced by Gourevitch and Saponov. I will describe these operators and discuss their relation with other constructions. I will also discuss the experimental data that supports the conjecture that one can define the quantum shift of the argument using these operators.
Bio: Georgy Sharygin got his PhD from Moscow State University in 2000, and since that time he has been teaching Mathematics at all levels from High school to the PhD programs. He was invited speaker at many international conferences, was many times invited researcher in various international institutes. His research interests include deformation quantisation, non commutative geometry, topology, differential geometry and integrable systems.
The category of 2D rational CFT's
Speaker：孔良（南方科技大学）
Time：2022年09月02日 21:0022:00
Meeting ID：腾讯会议 ID：939656494
点击链接入会：https://meeting.tencent.com/dm/aTqabg1ACJK5
Abstract: In this talk, I will review the categorical study of 2D rational CFT's and topological defects in the last two decades. In the end, I will show how to use it to describe the category of 2D rational CFT's.
Bio: 孔良，南方科技大学深圳量子科学与工程研究院研究员。1994年于中国科学技术大学获得物理学士学位，2005年于美国Rutgers，the State University of New Jersey获得数学博士学位。主要研究拓扑量子场论和共形场论的数学理论，以及在拓扑物质态中的应用。
可积系统中的Darboux变换简介
Speaker：刘青平（中国矿业大学）
Time：2022年08月19日 10:0011:00
Meeting ID：腾讯会议 ID：721493311
点击链接入会：https://meeting.tencent.com/dm/BnT3kqNexgYQ
Abstract: 这是关于Darboux变换的一个科普报告。我们将从Jean Gaston Darboux发表于1882年一篇短文谈起，介绍什么是Darboux变换、构造Darboux变换的方法以及它在可积系统理论中的应用。
Bio: 刘青平，国务院政府特殊津贴获得者，北京市高等学校教学名师，1992年获英国Leeds大学博士学位，曾在中国科学院理论物理研究所和西班牙Complutense大学做博士后，现为中国矿业大学（北京）教授。从事可积系统理论及其应用研究。更多信息见个人主页：https://lxy.cumtb.edu.cn/info/1067/1238.htm
Morse指标定理简介
Speaker：胡锡俊（山东大学）
Time：2022年08月12日 10:0012: 00
Meeting ID：腾讯会议 ID：324276209
点击链接入会：https://meeting.tencent.com/dm/syKSSjFXHH5R
Abstract: Morse指标定理源于对测地线的研究，它将Morse指标表为测地线共轭点的重数之和。在本次演讲中我们将回顾Morse指标定理的经典结论并介绍最新的进展。
Bio: 胡锡俊，山东大学教授。1997年7月和1999年7月在吉林大学分别获得学士学位和硕士学位，2002年7月在南开大学获得博士学位。2014年获得国家杰出青年基金，主要研究方向为哈密顿系统与非线性分析。在天体力学中周期解的稳定性问题，哈密顿系统指标理论及一类反应扩散方程行波解的研究中做出了创新性的工作。
Symmetries: from groups to tensor categories
Speaker：Alexei Davydov（Ohio University）
Time：2022年08月12日 16:0017: 00
Meeting ID：ZOOM ID：862 062 0549， Password：2022
点击链接入会：
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract: Groups are mathematical ways of talking about symmetries. From its beginning Group Theory was driven by the idea of symmetry and its applications (e.g. Galois' proof of unsolvability of a quintic). One of the most spectacular applications of Group Theory was the classification of crystals done at the end of the 19th century. In the middle of the 20th century Group Theory was used to describe all known states of matter. Experimental developments of the condensed matter physics at the end of the 20th century were not fitting the standard Group Theory scheme. They forced us to generalize the mathematical formulation of symmetry. The talk will be about this generalized notion, the one of tensor category.
Bio: Alexei Davydov is a Professor of Department of Mathematics, Ohio University. He mainly works on category theory and homological algebra.
Gravity properad, moduli spaces M_g,n, and string topology
Speaker：Sergei Merkulov University of Luxembourg
Time：2022年08月05日 16:0018: 00
Meeting ID：ZOOM ID：862 062 0549
Password：2022
点击链接入会：
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract: Using Thomas Willwacher’s twisting endofunctor, and Kevin Costello’s theory of partially compactified moduli spaces of algebraic curves of arbitrary genus with marked points, we introduce a new dg properad which contains Ezra Getzler’s operad controlling genus zero moduli spaces. We discuss its applications in the theory of moduli spaces M_g,n, and in string topology.
Bio: Sergei Merkulov is a Professor at the University of Luxembourg. He worked previously at the Russian Academy of Sciences, the Glasgow University (UK) and the Stockholm University (Sweden). He works on category theory, homological algebra and Differential geometry.
Thick morphisms of supermanifolds and homotopy algebras
Speaker：Theodore Voronov University of Manchester
Time：2022年07月29日 16:0018: 00
Meeting ID：ZOOM ID：862 062 0549
password：2022
点击链接入会：
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract: Supergeometry can be used as a unifying language for many algebraic and differentialgeometric constructions. Particular role here is played by homological vector fields, i.e. odd vector fields Q satisfying Q^2=0. They can be useful for describing “higher” or “homotopy” analogs of Poisson brackets. Recently I discovered a generalization of the notion of a smooth map (called by me “thick morphisms”) giving NONLINEAR pullbacks on smooth functions. “Thick morphisms” can in particular provide L_infinity morphisms for homotopy Poisson structures. There are other interesting connections, e.g. with Fourier integral operators. Thick morphisms also provide a nonlinear analog of classical functionalalgebraic duality.
Bio: Dr Theodore Voronov is a Professor in Pure Mathematics at the University of Manchester (UK). His research interests are on the crossroads of algebra, differential geometry, topology and mathematical physics; in particular, geometry of supermanifolds and its applications. See more at
http://personalpages.manchester.ac.uk/staff/theodore.voronov.
Representations of the FermionVirasoro algebras
Speaker：赵开明 Wilfrid Laurier University
Time：2022年07月15日 09:0011:00
Meeting ID：
腾讯会议 ID：635613814
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https://meeting.tencent.com/dm/aEOWDPUh24oM
Abstract: We introduce Fermion algebras F and the FermionVirasoro algebras. They are infinitedimensional Lie superalgebras. The progress on simple smooth modules and simple HarishChandra modules over these algebras will be discussed.
Bio: 赵开明，加拿大Wilfrid Laurier大学教授，主要研究方向为李代数。主持多项国家自然科学基金, 及加拿大NSERC基金。他在 Adv. Math., Tran. AMS, J. Lond. Math. Soc., J. Algebra 等国际刊物上发表学术论文100多篇。
RotaBaxter bisystems and mixed bialgebras
Speaker：Abdenacer Makhlouf（Université de Haute Alsace）
Time：2022年07月08日 16:0017:00
Meeting ID：
ZOOM ID：862 062 0549，Code：2022
会议链接：
https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract: In this talk, we deal with a generalization of the concept of RotaBaxter operators defined by T. Brzezi´nski and called RotaBaxter systems which appeared in [J. Algebra 460(2016):1 25]. We provide a dual version and then consider a generalization to bialgebras, we introduce the notion of RotaBaxter bisystem and construct various examples. On the other hand, we introduce a new type of bialgebras (named mixed bialgebras) which are consisting of an associative algebra and a coassociative coalgebra satisfying the compatible condition determined by two coderivations. We investigate coquasitriangular mixed bialgebras and the particular case of coquasitriangular infinitesimal bialgebras, where we give the double construction. This is a joint work with Tianshui Ma and Sergei Silvestrov.
Bio: Abdenacer Makhlouf is a Professor and the head of Mathematics Department at University of Haute Alsace, Mulhouse, France. His research covers structure, representation theory, deformation theory and cohomology of various types of algebras, including Nonassociative algebras, Hopf algebras and nary algebras.
KahlerRicci flow on smooth minimal models
Speaker：张振雷（首都师范大学）
Time：2022年07月01日 10:0012:00
Meeting ID：腾讯会议 ID：780765137
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Abstract: It is a survey talk on the longtime behavior of a KahlerRicci flow on a smooth manifold with a semiample canonical line bundle.
Bio：张振雷，首都师范大学数学科学学院教授。2003年本科毕业于吉林大学数学科学学院；2008年博士毕业于南开大学陈省身数学研究所，导师方复全教授。2018年获国家自然科学基金杰出青年科学基金资助，主要研究Ricci流、KahlerRicci流。
奇妙的基础数学
Speaker：徐晓平（中国科学院大学）
Time：2022年06月24日 14:0016:00
Meeting ID：腾讯会议 ID：703956224
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Abstract：这是一个科普型报告。我们从“什么是数学”谈起。然后是：素数的故事，拉马驽金的故事，分隔函数，KdV方程，量子物理的基本数学模型。之后，我们讲：数学的残缺美，一些挑战性问题以及本人的一些研究体验。
Bio：徐晓平，中国科学院大学教授，中国科学院数学研究所所长。1992年在美国Rutgers大学取得博士学位，师从著名的李理论专家James Lepowsky 和Robert Lee Wilson。之后在香港科技大学工作十年。2002年回到中国科学院数学研究所工作， 2014年开始兼任中国科学院大学教授，自2022年3月起，任中国科学院数学研究所所长。获宝钢优秀教师奖。他在李代数、顶点算子代数（共形场论）和偏微分方程的代数解法等相关领域的研究中做出了重要贡献。
低维拓扑学的世纪回顾
Speaker：雷逢春（大连理工大学）
Time：2022年06月24日 10:0012:00
Meeting ID：685963603
To Join Tencent Meeting: https://meeting.tencent.com/dm/49Yn9DtKVB4q
Abstract：拓扑学是当代核心数学的一个重要前沿领域，其渊源可追溯到欧拉早期的工作（1836年，哥尼斯堡七桥问题的解答）。拓扑学奠基于19世纪末, 在20世纪取得了梦幻般的发展, 进入21世纪更加兴旺发达。本报告将对拓扑学的发展作一个跨越世纪的通俗概要浏览, 重点介绍低维拓扑学的发展，即二、三和四维流形拓扑学的主要成就。
Bio：雷逢春，1990年12月博士毕业于吉林大学基础数学专业，研究方向为低维拓扑，现为大连理工大学数学科学学院教授、博士生导师。长期从事三维流形拓扑方面的研究工作，多次承担国家自然科学基金面上项目、重点项目和海外及港澳学者合作研究基金(延续)项目的研究工作。曾于1997年荣获国家教委科技进步二等奖(排名3)，2001年获黑龙江省杰出青年科学基金，2002年入选教育部“跨世纪优秀人才培养计划”。现为中国数学会常务理事，辽宁省数学会副理事长，大连市数学学会理事长。
Factorization of Shapovalov elements
Speaker：Andrey Mudrov（Moscow Institute of Physics and Technology and University of Leicester）
Time：2022年06月17日 15:0017: 00
Meeting ID：ZOOM ID：862 062 0549, Password:2022
Abstract：A classical result of J. Bernstein, I. Gelfand and S. Gelfand says that a singular vector in a Verma module over a simple complex Lie algebra can be obtained from its highest vector by applying a product of special elements of the negative nilpotent subalgebra called Shapovalov elements. We provide explicit formulas for those elements, and hence for singular vectors of the Verma modules, expressing them through certain matrix elements of the inverse contravariant Shapovalov form.
Bio：The speaker is currently an Associate Professor and a Senior Researcher at the Center of Fundamental Mathematics in MIPT, and an Honorary Lecturer at the University of Leicester. He is specializing in quantum groups, deformation quantization and related topics.
关于最对称的双曲环面上的闭测地线
Speaker：张影（苏州大学）
Time：2022年06月10日 10:0012:00
Meeting ID：564626700
To Join Tencent Meeting：https://meeting.tencent.com/dm/p7VBNfhblItm
Abstract：在与李祥飞的合作工作中，我们研究具有最大对称性的完备的双曲环面上的闭测地线的性质，证明一般闭测地线的迹多项式的正性，一些简单闭测地线长度的单调性，并提出简单闭测地线的迹的凸性猜测，以及一般闭测地线的迹多项式系数的对数凹性猜测。
Bio：张影，1985.91999.5 吉林大学数学系本研学习、任教，1999.52004.7 新加坡国立大学读研，2006.32007.2 巴西国家数学所(IMPA)博士后，2009.6至今，苏州大学数学科学学院教授。从事几何拓扑学研究。
同调论简史
Speaker：段海豹 (中国科学院数学与系统科学研究院)
Time：2022年5月27日 10:0012:00
Meeting ID：899680387
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Abstract：同调论是20世纪数学所诞生的一项新技术，是当代几何、拓扑、分析学的有力工具。报告通过 Riemann, Poincare, Brouwer, Hopf 等开拓者们的相关工作介绍，回顾同调论的背景、起源、以及发展历程。
Bio：段海豹，中国科学院数学与系统科学研究院研究员，1977年3月－1985年1月，在吉林大学数学系学习，获理学学士、硕士学位；1987年7月，在北京大学获博士学位。从事代数拓扑，微分拓扑和代数几何的教学、研究工作。 他在2005年获中国数学会陈省身数学奖，2010年获国家自然科学二等奖。
Lie 2algebras from geometric structures
Speaker：Zhangju LIU
Time：2022.5.13 14:0016:00
Meeting ID：347371151
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Abstract：The notion of Lie 2algebras is introduced as categorification of Lie algebras, Which is one of the fundamental objects in higher Lie theory and has close connection with strongly homotopy Lie algebras. The Lie 2algebra structure has enjoyed significant applications in both geometry and mathematical physics. Strict Lie 2algebras are equivalent to Lie algebra crossed modules, which are classified by the third cohomology of a Lie algebra.
In this talk, we’ll review several Lie 2algebras that come from geometric structures, namely, 2plectic manifolds; Courant algebroids; homotopy Poisson manifolds and affine structures on Lie groupoids. A 2plectic structure on a manifold is a nondegenerate closed 3form. There is a Lie 2algebra structure on functions and Hamiltonian 1forms of a 2plectic manifold A Courant algebroid is a vector bundle together with a bilinear form, a skewsymmetric bracket and an anchor map. The bracket satisfies the Jacobi identity up to a coboundary, which generates a Lie 2algebra on the section space of the bundle and functions on the base manifold. Parallel to the fact that there is a onetoone correspondence between Lie algebra structures on a vector space and linear Poisson structures on the dual space, there is a onetoone correspondence between Lie 2algebra structures on a 2vector space and linear homotopy Poisson structures on the dual 2vector space. On a Lie groupoid, vector fields that are compatible with the groupoid multiplication are called multiplicative. Multiplicative vector fields with the Schouten bracket form a Lie algebra, which is not invariant under the Morita equivalence of Lie groupoids. To define vector fields on a differentiable stack, one needs to extend the Lie algebra to a Lie 2algebra formed by affine vector fields on a Lie groupoid, which is Morita invariant.
Bio：刘张炬，北京大学/河南大学教授，1982年1月本科毕业于吉林大学，1986年6月在北京大学获得博士学位。1999年获得国家杰出青年基金。主要从事数学物理、Poisson几何等领域的研究。曾入选教育部跨世纪优秀人才支持计划，2004年获得教育部自然科学一等奖。
Morse matching method for conformal cohomology
Speaker：Pavel Kolesnikov (Sobolev Institute of Mathematics)
Time：2022.5.6 10:0012:00
Meeting ID：862 062 0549
Password：2022
To Join Zoom Meeting：https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract：We will observe the matching method in the algebraic discrete Morse theory which provides us a powerful tool for finding Anick resolutions for associative algebras defined by generators and relations. We apply this method to find reduced Hochschild cohomologies of associative conformal algebras in order to study their relations with the cohomologies of Lie conformal algebras. In particular, we evaluate the Hochschild cohomology groups for the universal associative envelope U(3) of the Virasoro Lie conformal algebra.
Bio：Pavel Kolesnikov got his PhD in 2002 in Novosibirsk State University (NSU) and joined Sobolev Institute of Mathematics. Now he is a research fellow of the Institute and professor in the NSU. His main area of research interests is in the structure and combinatorial theory of associative and nonassociative algebras, conformal and vertex algebras.
On the cobarconstruction for nonsimply connected spaces
Speaker：Andrey Lazarev ( Lancaster University )
Time：2022.04.22 16:0018:00
Meeting ID：862 062 0549
Password：2022
To Join Zoom Meeting：https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract：The cobarconstruction produces a differential graded (dg) algebra out of a dg coalgebra. When applied to the coalgebra of simplicial chains on a simplyconnected space X, the resulting dg algebra models the chain algebra on the based loop space of X. This is a classical result of Adams and it has been known for over 60 years. In a recent breakthrough development, American mathematicians Rivera and Zeinalian removed the simpleconnectivity assumption. In this talk, I will explain RiveraZeinalian’s result, discuss its generalizations and connections with infinitycategories.
Bio：Andrey Lazarev is a professor of pure mathematics in the University of Lancaster. His recent research deals with homotopy theory of differential graded algebras and categories, derived categories and higher phenomena. It has applications in rational homotopy theory, theory of operads and operadic algebras, algebraic topology and pure algebra. Andrey Lazarev is the Managing Editor of the journal《Bulletin of the London Mathematical Society》， as well as a Member of the Editorial Board of the journal《Higher_Structures》.
BosonFermion Correspondence and Its Applications to Integrable Hierarchies Revisited From The Point of View of Representation Theory and Random Walks
Speaker：Jian Zhou
Time：2022.04.15 10:0012:00
Meeting ID：694475243
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Abstract：We revisit the bosonfermion correspondence and its applications to integrable hierarchies via representation theory of symmetric groups. This makes it natural to consider random walks on various diagrams and graphs related to symmetric groups. Random partitions, hypergeometric taufunctions and weighted Hurwitz numbers are then brought together under a unified probabilistic treatment, rooted in their connections to the fermionic Fock space. Various approaches to the representation theory of symmetric groups all turn out to be useful in this treatment. They include: the new approach of Okounkov and Vershik, the Hopf algebra approach of Zelevinsky, and the lambdaring approach of Knutson. A connection to the interpolating statistics in the study of fractional quantum Hall effect will also be explained.
Bio：周坚，清华大学数学科学系教授，2005年国家杰出青年基金获得者、2009年入选国家“百千万人才工程”。他的研究领域为黎曼面的模空间与霍奇积分，拓扑场论，微分几何，弦理论等。周坚教授通过对超弦理论中Vafa学派的工作中出现的一些数学问题的研究，揭示了一些不同的数学分支之间的内在联系，他与合作者完成的“MarinoVafa猜想的证明”入选2004年度“中国高校十大科技进展”。
Heegaard splitting: a survey
Speaker: 邱瑞锋 (华东师范大学)
Time：2022年04月08日 10:0012:00
Meeting：#腾讯会议：680593921
https://meeting.tencent.com/dm/lxemeq0TOyx1
Abstract: Heegaard分解是紧致三维流形上普遍存在的组合拓扑结构，在三维流形理论的研究中起到了重要的作用。吉林大学是我国最早从事这一领域研究的研究群体，并直接或间接地培养了一批这一领域的专家学者。这个报告将介绍这一领域的国内外发展历史及现状。
Bio：邱瑞锋，华东师范大学教授，主要从事三维流形及纽结理论的研究，代表性工作有：（1）证明了Heegaard分解理论中的Gordon猜想，（2）构造了纽结洞数理论中的Morimoto猜想的反例等。
Orbifold theory and modular extensions
Speaker: 董崇英 美国加州大学Santa Cruz 分校
Time：20220325 10:0012:00
Abstract: Orbifold theory studies a vertex operator algebra V under the action of a finite automorphism group G. The main objective is to understand the module category of fixed point vertex operator subalgebra V^G. We prove a conjecture by DijkgraafPasquierRoche on V^G module category if V is holomorphic. We also establish a connection between rational orbifold theory and minimal modular extensions. Our work is based on the previous results on modular extensions by DrinfeldGelakiNikshychOstrik and LanKongWen. This is a joint work with Richard Ng and Li Ren.
Bio: 董崇英，美国加州大学Santa Cruz分校终身教授，国际上无限维李代数和顶点算子代数领域最杰出的数学家之一,多年来一直从事无穷维李代数、顶点算子代数、Orbifold理论以及广义月光等方面的研究。在Acta Math.、Duke Math. J.、Adv. Math.、Comm. Math. Phys.等国际著名期刊发表论文100多篇，总引用超过3000次，其中包括菲尔兹奖获得者Drinfeld、Zelmanov和Borcherds以及著名数学家如Beilinson和Kac等人的重要引用。主持多项美国自然科学基金，并担任杂志Algebra Colloquium的主编以及Science China Mathematics等多个杂志的编委。
Meeting：128767072加入会议：
https://meeting.tencent.com/dm/hyMIOAPeEsWf
Deformations of Symplectic Foliations
Speaker: Marco Zambon (KU Leuven)
Time: 2022.03.04 20:0022:00
Location： Zoom
ID：862 062 0549
Password：2022
Meeting：https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09
Abstract:
Symplectic foliations and regular Poisson structures are the same thing. Taking the latter point of view, we exhibit an algebraic structure that governs the deformations of symplectic foliations, i.e. which allows to describe the space of symplectic foliations nearby a given one. Using this, we will address the question of when it is possible to prolong a first order deformation to a smooth path of symplectic foliations. We will be especially interested in the relation to the underlying foliation. This is joint work with Stephane Geudens and Alfonso Tortorella.
Bio:
Marco Zambon is an associate professor at KU Leuven, Belgium. He works on topics related to Poisson geometry, in particular on those related to foliations, deformations and Lie theory.
Diophantine approximations
Speaker：Nikolay Moshchevitin (Moscow State University)
Location：Zoom
ID：894 9789 1576
Password：237198
Lecture1. Continued fractions.
2022.01.19， 13：3015：00
Representation of real numbers as continued fractions. Approximation by convergents, Perron's formula.
Irrationality measure function.
Lagrange and Dirichlet spectra. Minkowski diagonal continued fraction and the related spectrum. Geometry of continued fractions algorithm.
Lecture2. Distribution of Farey fractions.
2022.01.20， 13：3015：00
Elements of basic number theory. Euler and Moebius functions.
Integral representation of greatest common divisor. Counting the number of reduced fractions in [0,1].
Fraenel's theorem. Relation to Riemann zetafunction.
Lecture3. Farey tree and Minkowski function.
2022.01.26， 13：3015：00
SternBrocot sequences. Minkowski questionmark function.
Salem's theorem on the derivative. Fixed points problem. An analog to Fraenel's theorem.
FourierStieltjes coefficients.
Lecture4.Multidimensional approximation.
2022.01.27， 13：3015：00
Simultaneous approximation to real numbers. Linear forms close to xero.
Basic laws of approximation. Best approximations and phenomenon of degeneracy of dimension.
Diophantine exponents and Jarnik's inequalities.
Bio： Nikolay Moshchevitin教授现就职于莫斯科国立大学，研究兴趣为Geometry of numbers, geometric theory of Diophantine approximations, ergodic and combinatorial theory of numbers, theory of dynamical systems。共发表论文70余篇，超过400次引用。于1998年获得俄罗斯联邦国家奖。
Geometry of Gaussian random curves
Speaker：Andrey Dorogovtsev（Institute of Mathematics，NAS Ukraine）
Location：Zoom
ID：858 7772 7123
Password：803617
Abstract:
This course aims to provide a solid introduction on the geometry of Gaussian random curves. Since the theory of geometry of Gaussian random curves is based on the concept of Gaussian random process and fields, the first part of the course will be devoted to some properties of this process and fields. And the second part of the course is devoted to discussion of geometry of Gaussian random curves like the Selfintersection local times for planar Brownian motion and the hitting probabilities for planar Broownian motion. Professor Andrey will give students some time to understand the knowledge and give some small questions about the lecture.
Time：
Lecture 1: Gaussian random processes and fields. Main examples
In this lecture we give the definition of Gaussian random processes and fields. Also, we will give some examples to understand this.
Lecture 2: Smoothness of Gaussian random fields
In this lecture we discuss the smoothness of Gaussian random fields, and we can get some properties on Gaussian random fields.
Lecture 3: Euler characteristic of the subsets in Euclid space
In this lecture we give the definition of Euler characteristic which in defined on Euclid space, it is topological invariant.
Lecture 4: Rice formula and asymptotic of tales for supremum of Gaussian random fields
In this lecture we give the Rice formula and discuss the asymptotic of tales for supremum of Gaussian random fields.
Lecture 5: Trajectory of Brownian motion as a random curve. Basic properties
In this lecture we discuss the trajectory of Brownian motion and give some basic properties about this.
Lecture 6: Selfintersection local times for planar Brownian motion
In this lecture we discuss the investigation of the local times of selfintersection as the most important geometric characteristics for planar Brownian motion.
Lecture 7: Hitting probabilities for planar Brownian motion
In this lecture we discuss the hitting probabilities and how we use this to describe the trajectory of planar Brownian motion.
Lecture 8: Tube formula for planar Brownian motion
In this lecture we give the Tube formula for planar Brownian motion, and use it to help us learn the trajectory of Brownian motion.
Bio：
Andrey Dorogovtsev教授是乌克兰国家科学院通讯院士，乌克兰国家科学院数学所随机过程理论系主任，主要从事概率论及其相关领域研究，是乌克兰概率论研究方向学术领军人物之一。Andrey Dorogovtsev教授是乌克兰与德国、乌克兰与俄罗斯等国家联合项目的乌方负责人。同时，Andrey Dorogovtsev教授是《Theory of Stochastic Processes》、《Ukraine Mathematical Journal》等杂志的编委。
Knot theory
Speaker：Vassily Olegovich Manturov（Moscow Institute of Physics and Technology）
Time：2022年1月
Location：Tencent Meeting
Room Number:61495481864
Password：372633
Abstract:
Lecture1.
Reidemeister moves. Colouring invariants, and the linking number.
2022/01/06 18:0019:00
Abstract:
We will introduce diagrams of knots and links. We use the diagrams to build two invariants of links: Coloring invariant and the linking number.
Lecture2.
The Kauffman bracket, the Jones polynomial.
2022/01/09 18:0019:00
Abstract:
We will use Kauffman bracket to prove that Jones polynomial is a link invariant.We will compute some examples and prove the KauffmanMurasugiThistlethwaite Theorem.
Lecture3.
Fundamental group. The knot group.
2022/01/13 18:0019:00
Abstract:
We will define a famous link invariant: the fundamental group of the knot complements. We will show that this group is not trivial if the knot is not trivial.
Lecture4.
The knot Quandle is a complete knot invariant.
2022/01/16 18:0019:00
Abstract:
Matveev and Joyce defined a knot invariant, the knot quandle. This is a complete invariant. We can obtain many invariants from the knot quandle, for example, the knot group and coloring invariant.
Lecture5.
The braid groups
2022/01/20 18:0019:00
Abstract:
We define the braid group. The action of the braid group on Aut(F_{n}) is complete.We will also discuss Markov Theorem and Alexander Theorem.
Lecture6.
The Alexander polynomial.
2022/01/23 18:0019:00
Abstract:
We will introduce several ways to define the Alexander polynomial.
Lecture7.
Vassiliev invariant
2022/01/27 18:0019:00
Abstract:
We will introduce the Vassiliev invariant and prove that “polynomial” invariant are all come from the Vassiliev invariant.
Lecture8.
Khovanov homology
2022/01/30 18:0019:00
Abstract:
Khovanov homology is a categorification of the Jones polynomial, in the sense that its Euler characteristic is the Jones polynomial.
Bio：Professor Vassily Olegovich Manturov is from Moscow Institute of Physics and Technology. His research interest is low dimensional topology and knot theory. He has published more than 150 papers and got more than 1500 citations. He got "Professor of RAS" in 2016 and he is one of the Managing Editors of the "Journal of Knot Theory and Its Ramifications". He has published many books, for instance, 《Parity in knot theory and graphlinks. Contemporary Mathematics. Fundamental Directions》，《Lowdimensional Topology and Combinatorial Group Theory》，《Virtual Knots. The State of the Art》 and 《Knot Theory》. He held many international conferences, such as "4th Russian China RussiaChina on Knot theory and Related topics" and three International Conferences in the Mathematical Institute (Oberwolfach) on knot theory and lowdimensional topology".
RotaBaxter operators, skew braces and YangBaxter equation
Speaker：Valeriy Bardakov
Time：2021.12.17 15:0017:00
Location：Zoom
Meeting ID: 862 062 0549
Password: 2021
Meeting：https://us02web.zoom.us/j/8620620549?pwd=NUhCMWpuTG9Od1RMNjhEdkdwTzlsUT09
Abstract:
Bio：Valeriy Bardakov is a professor of Sobolev Institute of Mathematics with holding a joint position at Laboratory of Topology and Dynamics of Novosibirsk State University. Valeriy Bardakov is a famous expert on braid theory, knot theory and group theory with over 90 publications in the area.
Variational Bihamiltonian Cohomology and Integrable Hierarchie
Speaker：Youjin Zhang(Tsinghua University)
Time：2021.12.10 10:0012:00
Location：Meeting Tencent
Meeting ID：924966280
Meeting：https://meeting.tencent.com/dm/4PgMu2SMQi39
Abstract: In order to study deformations of Virasoro symmetries of the bihamiltonian integrable hierarchies associated to semisimple Frobenius manifolds, we introduce the notion of variational bihamiltonian cohomology, and compute the cohomology groups that will be used in our study of deformations of Virasoro symmetries. To illustrate its application, we classify the conformal bihamiltonian structures with semisimple hydrodynamic limits.
Bio：张友金，清华大学数学科学系教授，杰出青年基金获得者，教育部长江学者特聘教授。1994年于中国科技大学数学系获博士学位，19901991年在俄罗斯斯捷克洛夫数学所圣彼得堡分所作访问学者，19941999年在意大利国际理论物理中心、意大利国际高等研究院和日本京都大学数学系从事博士后研究，1999年起任清华大学数学科学系教授。主要从事数学物理与可积系统理论方面的研究，在双哈密顿可积方程簇的分类及其与Frobenius流形、GromovWitten不变量理论的联系等方面做出了重要的工作。在Invent. Math., CMP, Adv. Math.等顶尖杂志上发表学术论文50余篇。
Ooperators on Lie infinity algebras
Speaker：Joana Nunes da Costa（University of Coimbra  Portugal）
Time：2021.12.03 16:0018.00
Location：Zoom
ID：862 062 0549
Password：2021
ZOOM meeting：https://us02web.zoom.us/j/8620620549?pwd=NUhCMWpuTG9Od1RMNjhEdkdwTzlsUT09
Abstract: We define Ooperators on a Lie infinity algebra E with respect to an action of E on another Lie infinity algebra. We characterize these operators as MaurerCartan elements of a certain Lie infinity algebra obtained by Voronov's higher derived brackets construction. We determine the Lie infinity algebra that controls the deformation of Ooperators with respect to a fixed action.
Bio：Joana Nunes da Costa is a professor of University of Coimbra, Portugal. She mainly works on Poisson geometry and mathematical physics.
The LangTrotter Conjecture and the HardyLittlewood Conjecture
Speaker：Hourong Qin（Nanjing University）
Time：2021.11.26 09:0011.00
Location：Meeting Tencent
Meeting ID：662 784 567
Meeting：https://meeting.tencent.com/dm/qloVYRjPFHvl
Bio： 秦厚荣教授现任南京大学数学系系主任，江苏国家应用数学中心主任，中国数学会常务理事，中国科学数学编委，江苏省数学学会第十届，十一届理事长，第十二届监事会主席。1999年获得国家杰出青年基金，2004年受聘教育部长江学者计划特聘教授，首批入选国家“百千万人才计划”（2004年），享受国务院特殊津贴。他的研究方向主要是代数数论和代数K理论。他在同余数这一历史悠久问题上的研究上取得了重要成果；在数域的Tame核、Tate核方面做出了原创性工作，引发了大量后续工作；解决了田野，Browkin等人的多个猜想；在著名的椭圆曲线Anomalous素数的Mazur猜想以及LangTrotter猜想的研究中取得了突破。他在J. Reine Angew Math., P. London Math. Soc., Math. Ann. 等国际著名刊物上发表了数十篇论文，研究结果在国际同行中产生了广泛而积极的影响，被国外同行称为“秦的方法”，多次在高水平国际学术会议上作大会邀请报告。
Quantum GIM of Nfold affinization and quantum toroidal algebra
Speaker：Yun Gao（York University）
Time：2021.11.19 09:0011.00
Location：Zoom
Meeting ID：862 062 0549
Password：2021