Set-theoretic Yang-Baxter equation, twists & quandle Hopf algebras

Speaker: Anastasia Doikou (Heriot-Watt University)

Time: November 21, 2024   20:30-22:30

Venue: ZOOM ID：904 645 6677,   Password：2024

Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456

Abstract: The theory of the set-theoretic Yang-Baxter equation is established from a purely algebraic point of view. The derivation of solutions of the braid equation via certain self-distributive structures called racks and quandles is reviewed. Generic, non-involutive set-theoretic solutions of the braid equation are then obtained from rack solutions by a suitable Drinfl'd twist, whereas all involutive solutions are obtained from the flip map via a twist. The universal algebras associated to both rack and generic set-theoretic solutions are also studied and the corresponding universal R-matrices are derived. 

Bio: Anastasia Doikou is a Professor of Mathematics at Heriot-Watt University in Edinburgh. She studied physics as an undergraduate at National & Kapodistrian University of Athens and she obtained her PhD in theoretical and mathematical physics from University of Miami in 1999. Between 1999 and 2007 she held postdoctoral positions at Durham University, University of York (EPSRC Fellow), LAPTH-Annecy and University of Bologna. She was assistant professor at University of Patras in Greece before joining Heriot-Watt University in 2013.

Previous lectures and talks:

Reflection vectors, monodromy data and Dubrovin conjecture

Speaker: John Alexander Cruz Morales (Universidad Nacional de Colombia)

Time: November 13, 2024   16:00-18:00

Venue: 吉林大学数学楼第五研讨室

Abstract: Using the notion of reflection vectors (which only depends on the second structure connection) I will show how to get explicitly the Stokes and central connection matrices for a semisimple Frobenius manifold. In the case of quantum cohomology, I will discuss some implications for the so-called Dubrovin conjecture which relates the quantum cohomology of a (Fano) manifold with its bounded derived category of coherent sheaves. This is a joint work with Todor Milanov.

Bio: John Alexander Cruz Morales is an associate professor at Universidad Nacional de Colombia. He is mainly interested in mirror symmetry and related topics such as derived categories, integrable systems and representation theory. 

Deformations of Symplectic Foliations

Speaker: Alfonso Giuseppe TORTORELLA (University of Salerno)

Time: November 07, 2024   20:00-21:00

Venue: ZOOM ID：904 645 6677,   Password：2024

Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456

Abstract: In this talk, based on joint work with Stephane Geudens and Marco Zambon, we develop the deformation theory of symplectic foliations, i.e. regular foliations equipped with a leafwise symplectic form. The main result is that each symplectic foliation is attached with a cubic L∞algebra controlling its deformation problem. Indeed, we establish a one-to-one correspondence between the small deformations of a given symplectic foliation and the Maurer–Cartan elements of the associated L∞ algebra. Further, we prove that, under this one-to-one correspondence, the equivalence by isotopies of symplectic foliations agrees with the gauge equivalence of Maurer–Cartan elements. Finally, we show that the infinitesimal deformations of symplectic foliations can be obstructed. 

Bio: Alfonso Giuseppe TORTORELLA received his PhD from the University of Florence in 2017, and is currently an Assistant Professor of Geometry at the University of Salerno. His research focuses on the geometry of Poisson and related structures, and studies mainly deformation problems in Poisson geometry.

Desingularizing singular symplectic structures

Speaker: Eva Miranda (Polytechnic University of Catalonia)

Time: October 18, 2024   20:00-22:00

Venue: ZOOM ID：904 645 6677,   Password：2024

Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456

Abstract: The exploration of symplectic structures on manifolds with boundaries has naturally led to the identification of a “simple” class of Poisson manifolds. These manifolds are symplectic away from a critical hypersurface, but degenerate along this hypersurface. In the literature, they are referred to as b-symplectic or log-symplectic manifolds. They arise in the context of the space of geodesics of the Lorenz plane and serve as a natural phase space for problems in celestial mechanics such as the restricted 3-body problem. Geometrically, these manifolds can be described as open symplectic manifolds endowed with a cosymplectic structure on the open ends.

The technique of "deblogging" or desingularization associates a family of symplectic structures to singular symplectic structures with even exponent (known as b^{2k}-symplectic structures), and a family of folded symplectic structures for odd exponent (b^{2k+1}-symplectic structures). This method has good convergence properties and generalizes to its odd-dimensional counterpart, contact geometry. In this way, the desingularization technique puts under the same umbrella various geometries, such as symplectic, folded-symplectic, contact, and Poisson geometry.

The desingularization kit has a broad range of applications, such as the construction of action-angle coordinates for integrable systems, KAM theory, quantization, and counting periodic orbits.

Bio: Eva Miranda is Chair in Geometry and Topology in the Department of Mathematics at the Polytechnic University of Catalonia, and a member of CRM.  She has been a visiting professor at the Paris Observatory, MIT, the University of Toulouse, and the University of Paris 7, and she was an honorary professor at CSIC and an Affiliate Researcher at the Paris Observatory. Miranda is the director of the Geometry and Dynamical Systems Laboratory at UPC and the leader of the Geometry of Manifolds and Applications research group at UPC.

Miranda has been awarded two consecutive ICREA Academia prizes (in 2016 and 2021), a Chair of Excellence from the Paris Mathematical Sciences Foundation in 2017-2018, a Bessel Award from the Humboldt Foundation in 2022, and the François Deruyts Prize in 2022. She was invited speaker at the 8ECM. She was named Hardy Lecturer 2023 by the London Mathematical Society and Nachdiplom Lecturer 2025 by ETHZ. In 2024, she was appointed Gauss Professor by the University of Göttingen.

A post-group theoretic perspective on the operator-valued S-transform in free probability

Speaker: Kurusch Ebrahimi-Fard (Norwegian University of Science and Technology)

Time: October 10, 2024   20:00-22:00

Venue: ZOOM ID：904 645 6677,   Password：2024

Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456

Abstract: We discuss the algebraic structure underlying Voiculescu's S-transform in operator-valued free probability. It is shown how its twisted factorisation property gives rise to post-groups, crossed morphisms, as well as pre- and post-Lie algebras. Based on joint work with T. Ringeard (arXiv:2402.16450).

Bio: Kurusch Ebrahimi-Fard earned his Ph.D. in Theoretical Physics from the University of Bonn under the supervision of D. Kreimer and R. Flume. He also hold a Maîtrise de Mathématiques from Université Joseph Fourier in Grenoble, France. His past academic roles include postdoctoral positions at the Institut des Hautes Études Scientifiques (IHES, Bures-sur-Yvette, France), the Max Planck Institute for Mathematics (MPIM, Bonn, Germany), Universidad de Zaragoza (Zaragoza, Spain), and Instituto de Ciencias Matemáticas (ICMAT, Madrid, Spain), as well as an associate professorship (Maître de Conférences) at Université de Haute-Alsace (Mulhouse, France). Since 2016, He has been working in the Department of Mathematical Sciences at the Norwegian University of Science and Technology (NTNU) in Trondheim, Norway. He was awarded both the Juan de la Cierva and Ramón y Cajal fellowships. Additionally, he was a fellow of the Studienstiftung des Deutschen Volkes, the Evangelisches Studienwerk e.V., the German Academic Exchange Service (DAAD), and the European Post-Doctoral Institute (EPDI).

NL bialgebras

Speaker: Zohreh Ravanpak (University of Timișoara)

Time: September 26, 2024   15:30-16:30

Venue: 吉林大学数学楼第五研讨室

Abstract: In this talk we introduce the concept of (weak) NL bialgebras. It explores the Poisson-Nijenhuis structures on manifolds within the context of Lie bialgebras.  These structures contribute to understanding the interplay between Nijenhuis operators and Lie bialgebras satisfying specific compatibility conditions.  They reveal how compatibility conditions facilitate the construction of a hierarchy of compatible Lie bialgebras, both on the original Lie algebra and on its deformed versions through the Nijenhuis structure of any order. We apply our findings to a well-known dynamical system, a particular case of the Euler-top, demonstrating that the underlying algebraic structure of Euler-top dynamics is a weak NL bialgebra. It is based on my recent work: https://arxiv.org/pdf/2404.17708.

Bio: Zohreh Ravanpak completed her PhD in 2018 in Iran, which included a doctoral internship at WSMCS in Warsaw and a six-month research stay at the University of La Laguna (ULL) in Spain. After that, She was a postdoctoral researcher at the Polish Academy of Sciences in Warsaw and the Max-Planck Institute for Mathematics in Bonn. Currently, She is a young researcher at the University of Timișoara în România. Her research focuses on differential geometry and mathematical physics, particularly in the areas of integrable systems (Hamiltonian and bi-Hamiltonian), Poisson geometry, Lie theory, and Lie groupoids.

Symmetric polynomials and identities for n-Lie dialgebras

Speaker: Askar Dzhumadil'daev (Kazakh-British Technical University)

Time: September 21, 2024   14:10-15:10

Venue: 吉林大学正新楼209

Abstract: Polynomial identities for n-Lie dialgebras constructed by symmetric polynomials are studied. Constructions are depend from transposed Poisson structures. 

Bio: Askar Dzhumadil'daev is a professor of Kazakh-British Technical University, full member of the Kazakhstan National Academy of Science. His research interests concern cohomologies and deformations of Lie algebras, N-commutators of vector fields, identities of non-associative 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   8:30-9:30

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, non-commutative 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 Ayupov-Kadison-Liu 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 Non-associative 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) (2015-2021). 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.

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 Yang-Mills 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   20:00-22:00

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 Killing-type trace-form 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   11:00-13:00

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 Clermont-Auvergne in France. She received her PhD at the Ruhr University in Bochum. She works in mathematical physics using tools borrowed from pseudo-differential analysis, geometry and number theory.

Separable Volterra operators and generalized Reynolds algebras

Speaker: Li Guo (Rutgers University-Newark)

Time: August 23, 2024   11:00-13:00

Venue: 吉林大学数学楼第6研讨室

Abstract: The Reynolds operator originated from the well-known 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 D-differential 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Rota-Baxter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Rota-Baxter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。

S-curvature of homogeneous Finsler spaces

Speaker: Shaoqiang Deng (南开大学数学科学学院)

Time: August 16, 2024   14:00-16:00

Venue: 吉林大学数学楼第5研讨室

Abstract: In this talk, we present our recent results on S-curvature of homogeneous Finsler spaces. We show that a geodesic orbit Finler spaces has vanishing S-curvature. Then we construct some examples of reversible non-Berwald spaces with vanishing S-curvature. We present an explicit formula of the S-curvature of homogeneous Randers spaces, and give a complete classification of homogeneous Randers spaces with positive flag curvature and vanishing S-curvature.

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2013-2017和2018-2022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 anti-pre-Lie bialgebras

and anti-pre-Lie-Poisson bialgebras

Speaker: Chengming Bai (南开大学陈省身数学研究所)

Time: August 13, 2024   15:00-16:00

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 2-cocycles on the Lie algebras instead. Explicitly, we first introduce the notion of anti-pre-Lie bialgebras as the equivalent structure of Manin triples of Lie algebras with respect to the commutative 2-cocycles. Then we introduce the notion of anti-pre-Lie 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 2-cocycles 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   9:00-10:00

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 Li-Sheng 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   9:30-10:30

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   20:00-21:00

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 self-contained. 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 non-linear differential equations and applications in hydrodynamics.

Integrable Peakon Models and Beyond

Speaker: Zhijun Qiao (University of Texas Rio Grande Valley)

Time: June 22, 2024   16:00-17:00

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 b-family quadratic and cubic peakon models (FORQ, MOCH, Novikov Equations etc) with peakon and weak-kink solutions. We will also talk about a new CH-type equation – fifth-order CH equation and present new type solutions – pseudo-peakon 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。1999-2001，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   15:30-16:30

Venue: 吉林大学正新楼209

Abstract: 扭Heisenberg-Virasoro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   20:00-21:00

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 post-Hopf algebras and weak twisted relative Rota-Baxter operators. The latter objects are a generalisation of the relative Rota-Baxter operators where the Rota-Baxter condition is modified through a cocycle. Also we will present the notion of generalized invertible 1-cocycle and we prove that the category of Hopf trusses is equivalent to the category of generalized invertible 1-cocycles. On the other hand, we also introduce the notions of module for a Hopf truss and for a generalized invertible 1-cocycle. We prove some functorial results involving these categories of modules and we show that the category of modules associated to a generalized invertible 1-cocycle is equivalent to a category of modules associated to a suitable Hopf truss. Finally, assuming the existence of equalizers, we introduce the notion of Hopf-module 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 08-17, 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 point-supported singular perturbations of the free operator. This point-like perturbation is given as point-source 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 Photo-Acoustic imaging.

Two scenarios are discussed here. In the first one, we use isolated (or closely-spaced) contrast agents. Two general ideas can be highlighted in this case depending whether we use time-harmonic or time- domain measurements:

1.  Time-harmonic 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.  Time-domain case. Looking at the measured fields in terms of time, we can recover the internal values of the travel-time function. This travel-time function provides us the values of the speed of propagation by solving the Eikonal equation.

In the second scenario, these agents are used all-at-once, as a cluster. In this case, we show that we can linearize the boundary maps, as the Neumann-Dirichlet 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 third-party 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 co-edited 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).

L-Algebras: The Yang-Baxter equation in algebraic logic

Speaker: Leandro Vendramin (Vrije Universiteit Brussel，Belgium)

Time: April 23, 2024   20:00-22:00

Venue: ZOOM ID：904 645 6677,   Password：2024

Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456

Abstract: We will discuss interactions between set-theoretical solutions to the Yang-Baxter equation and structures that appear in algebraic logic. Most of this interplay will be based on the recently introduced theory of L-algebras. Hilbert and Heyting algebras are examples of L-algebras. 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 Yang-Baxter equation. This includes Hopf algebras and Nichols algebras and discrete structures such as skew braces and L-algebras. 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   20:00-21:00

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 well-known that this associator has applications to the quantization of (quasi) Lie bialgebras (P.I.Etingof-D.A.Kazhdan and B.Enriquez-G.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 star-shaped domains of the real line and plane with respect to explicit flat (formal) connections derived from the Knizhnik-Zamolodchikov 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   16:00-17:00

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; Groubner--Shirshov 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 Groubner-Shirshov 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   20:00-22:00

Venue: ZOOM ID：904 645 6677,   Password：2024

Abstract: Historically, (skew) braces are algebraic structures that arose out of the study of set-theoretic solutions of the Yang-Baxter 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 Yang-Baxter 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 Yang-Baxter equation, but also unveiled unexpected connections with for example Hopf-Galois extensions, pre-Lie rings and post-Lie 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 Hopf-Galois extensions, set-theoretic solutions of the Yang-Baxter equation and pre-Lie rings.

Rota-Baxter operators on groups

Speaker: Aleksei Galt (Sobolev Institute of Mathematics)

Time: March 21, 2024   15:30-16:30

Venue: The fifth seminar room, Mathematics Building

Abstract: Rota-Baxter 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 Rota-Baxter operators on groups. We describe all Rota-Baxter 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   20:00-22:00

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 co-author of a monograph and over 110 papers (written with ca 45 co-authors). 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   20:00-22:00

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 quasi-Poisson structure. The smooth locus of this variety carries a corresponding symplectic form defined by D. Yamakama through quasi-Hamiltonian 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 (non-degenerate) Hamiltonian quasi-Poisson 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 non-commutative Poisson geometry. Time allowing, I may comment on  the application of this result to the spin Ruijsenaars-Schneider phase space; this shows the compatibility of two Poisson structures that appeared in independent works of Arutyunov-Olivucci (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) non-commutative Poisson geometry.

Modular classes in Poisson and Jacobi geometry

Speaker: Aissa Wade (Penn State University, USA)

Time: February 22, 2024   21:00-22:00

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 post-groups, post-groups from group actions and post-Lie algebras 

Speaker: Dominique Manchon (Université Clermont-Auvergne)

Time: February 01, 2024   20:00-21:00

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 post-group by C. Bai, L. Guo, Y. Sheng and R. Tang, we will exhibit post-group and weak post-group counterparts of important post-Lie algebras in the literature, including the infinite-dimensional post-Lie algebra of Lie group integrators. The notion of free post-group will be examined, and a group isomorphism between the two group structures associated to a free post-group, reminiscent to A. Gavrilov's K-map in differential geometry, will be described. This is a joint work with Mahdi Jasim Hasan Al-Kaabi (Mustansiriyah University, Baghdad, Iraq) and Kurusch Ebrahimi-Fard (NTNU, Trondheim, Norway).

Bio: Dominique Manchon Chargé de Recherches (senior researcher) at CNRS, Laboratoire de Mathématiques Blaise Pascal, Université Clermont-Auvergne, Clermont-Ferrand, 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   9:00-11:00

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   20:00-21:00

Location: ZOOM ID：904 645 6677,   Password：2023

Abstract: In the last few years, several generalizations of classical objects (associative, dendriform, pre-Lie, Rota-Baxter 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, Xiao-Song 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   20:00-21:00

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 long-standing 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.

Rota-Baxter operators and coboundary Lie bialgebra structures on perfect finite-dimensional Lie algebras

Speaker: Maxim Goncharov (Sobolev Institute of Mathematics)

Time: December 1, 2023   13:00-14:00

Location: 313 Zhengxin Building

Abstract: There is a connection between structures of a Lie bialgebra on a given quadratic Lie algebra L and Rota-Baxter 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 one-to-one correspondence with skew-symmetric Rota-Baxter operators of weight zero on L. Another classical result states the connection between factorizable Lie bialgebra structures and Rota-Baxter operators of weight 1 satisfying some generalized skew-symmetry 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 Yang-Baxter equation and Rota-Baxter operators of special type. Also, we will describe the classical double of a coboundary Lie bialgebra in terms of Rota-Baxter operators. As an application, we will speak on coboundary Lie bialgebra structures on simple, semisimple, and reductive finite-dimensional 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   11:00-12:00

Location: 313 Zhengxin Building

Abstract: The inverse scattering method, as well as the r-matrix 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   13:30-14:30

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 non-associative 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 Q-manifolds) and present a normal for result for a homological vector field on Z-graded 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 13-16, 2023   21:00-22:00

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   10:00-11:00

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 top-ranked international journals, Xiaoping has co-edited 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 pseudo-Hermitian metrics

Speaker: Ignacio Bajo (Universidad de Vigo, Spain)

Time: October 26, 2023   20:00-21:00

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 pseudo-Hermitian 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 Lorentz-Hermitian and to obtain a complete classification of pseudo-Hermitian quadratic Lie algebras up to dimension 8 and their inequivalent pseudo-Hermitian 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 non-associative 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 Yang-Baxter operators and Lie algebra cohomology

Speaker: Emanuele Zappala (Idaho State University)

Time: October 19, 2023   20:00-21:00

Location: Zoom ID：904 645 6677     Password：2023

Abstract: Self-distributive objects in symmetric monoidal categories are known to produce Yang-Baxter operators, e.g. quandles and their linearization in modules. An important class of self-distributive objects arises from Lie algebras (binary and $n$-ary as well), giving a way of constructing a Yang-Baxter operator from an initial Lie algebra. This allows us to study the relation between self-distributive cohomology, Lie algebra cohomology, and Yang-Baxter cohomology. We therefore obtain a theory of infinitesimal deformations of Yang-Baxter operators that is tightly connected to the deformation theory of Lie algebras and their associated self-distributive 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 Yang-Baxter operators in relation to the higher deformations of Lie algebras, therefore producing Yang-Baxter 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 (Yang-Baxter 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 20:00-21:00

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 17:00-18:00

Location: Zoom ID: 904 645 6677  Password:2023

Abstract: Complex manifolds can be characterized as pairs (M,J), where M is an even-dimensional 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 8-dimensional real nilpotent Lie algebra having one-dimensional 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 non-Kähler geometry, although she is also interested in topics related to Lie algebras and Lie groups.

Pre-Lie algebra structures and etale affine representations

Speaker: Dietrich Burde (University of Vienna, Austria)

Time: September 14, 2023 20:00-21:00

Location: Zoom ID: 904 645 6677  Password:2023

Abstract: Pre-Lie algebras and Post-Lie 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 Young-Baxter 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 pre-Lie algebra structure on the associated Lie algebra. Pre-Lie algebra structures also correspond to left-invariant 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 Lie-algebraic Structures".

Semidirect products in digroups, skew braces, heaps, trusses, and in universal algebra

Speaker: Alberto Facchini (University of Padua)

Time: September 7, 2023 20:00-21:00

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 Yang-Baxter 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 10:30-11:30

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 AS-Gorenstein 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 21-25, 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 Keller-Lefevre 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。

On the volume of hyperbolic tetrahedron

Speaker: Nikolay Abrosimov (Sobolev Institute of Mathematics of RAS)

Time: August 20, 2023 10:30-11:30

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, 3-orthogonal 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 4-parameter 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 metrico-proiettivi // 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 Mechanics-Mathmatics 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 non-Euclidean polytopes, geometry and topology of three-dimensional 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 09:30-10:30

Location: 正新楼313室

Abstract: A polyhedron in a three-dimensional 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 one-dimensional skeleton G is equal to the volume of an ideal right-angled hyperbolic polyhedron whose one-dimensional 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 three-dimensional manifolds”, and a Doctor of Sciences in physics in mathematics in 2005 for the thesis “Volumes and isometries of three-dimensional hyperbolic manifolds and orbifolds”.

    Professor Vesnin's research interests include low-dimensional 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.

Yang-Baxter equation, Rota-Baxter operators and corresponding algebraic systems

Speaker：Valeriy Bardakov （Tomsk State University）

Time：2023年6月28日 14:30-15:30

Location：吉林大学数学楼3楼第5研讨室

Abstract: Yang-Baxter 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 n-simplex equation. To describe solutions of these equations where introduced different algebraic systems: rack, quandle, skew brace and some other. The Yang-Baxter equation connects with Rota-Baxter 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 Mechanic-Mathematics, 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 13:30-14:30

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 2-sphere.  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 Mechanic-mathematics, Tomsk State University. Her research interests are 3-dimensional topology, theory of 3-manifolds, low-dimensional 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 18:00-20:00

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 `odd-dimensional generalizations’ of symplectic geometry but rather particular examples of symplectic geometry, namely homogeneous symplectic principal bundles (with an action of the multiplicative group of non-zero 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 Hamilton-Jacobi 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 K-theory of discrete groups

Speaker：Bailing Wang （The Australian National University）

Time：2023年5月19日 10:30-11:30

Meeting ID：腾讯会议：516-539-518

Abstract:  In the 1980’s motivate by the Atiyah-Singer index formula,  Baum and Connes constructed a  topological K-theory of a discrete group  $\Gamma$, together with  an assembly map $\mu$  from this mysterious group to the K-theory 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, Gromov-Lawson-Rosenberg conjecture and Kadison-Kaplansky conjecture.                     

The mathematical details of this construction and the well-definedness 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 Chern-Connes 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 15:50-16: 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 two-form and a three-form on the corresponding Lie algebroid. If the two-form is non-degenerate, it defines a pseudo-Riemannian metric on the Lie algebroid and a family of Lie algebroid torsion-free connections, including the Levi-Civita connection of the metric. In this framework, the standard two-point 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 20:00-22:00

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 so-called 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 Rota-Baxter 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 group-theoretical aspects of skew braces.

On pseudo-Euclidean Lie algebras whose Levi-Civita product is left Leibniz

Speaker：Said Benayadi （University of Lorraine-Metz）

Time：2023年3月30日 20:00-21:00

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 pseudo-Euclidean metric such its Levi- Civita product is left Leibniz. We call them Levi-Civita left Leibniz Lie algebras LCLL for short. We show that a Lie group (G, h) endowed with a left invariant pseudo-Riemannian 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 Lorraine-Metz. His research interest is nonassociative algebras.

Singular foliations and Q-manifolds

Speaker：Camille Laurent-Gengoux （Université de Lorraine, Metz）

Time：2023年3月22日 16:00-17: 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 Q-manifold (equivalently, a Lie infinity algebroid) can be associated to a singular foliation, and how this Q-manifold helps in studing the geometry of the latter. Joint works with Sylvain Lavau, Ruben Louis,  Leonid Ryvkin, Thomas Strobl.

Bio: Camille Laurent-Gengoux 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 University-Camden）

Time：2023年3月9日 09:00-10:00

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 one-to-one 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 University-Camden. 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 φ-coordinated 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 21:00-22:00

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 non-integrability 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 2-local derivations and automorphisms of Octonian algebras 

Speaker：Shavkat Ayupov (Institute of Mathematics, Uzbekistan Academy of Sciences)

Time：2023年2月9日 16:00-17:00

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 2-local 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 skew-symmetric 7 × 7-matrices over F. At the same time the Lie algebra of all derivations are isomorphic to the exceptional Lie algebra g₂(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 2-local derivations on the octonion algebra O(F) over an algebraically closed field F and prove that every 2-local derivation on O(F) is a derivation. But for the field R of real numbers 2-local derivations on the octonian algebra O(R) form a Lie algebra which is essentially larger than   the Lie algebra g₂(R) of derivations. we apply these results to problems for the simple 7-dimensional 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 O₇(F) of all orthogonal 7 × 7-matrices over F, and it is essentially larger than the group of all automorphisms.

We also consider 2-local automorphisms on the octonion algebra O(F) over an algebraically closed field F and prove that every 2-local automorphism on O(F) is an automorphism. At the same time the group of 2-local automorphisms of O(R) is larger than the group of automorphisms of O(R). As a corollary we obtain descriptions of local and 2-local 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 Non-associative 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) (2015-2021). 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 Koszul-Tate resolutions and BFV for singular coisotropic reductions 

Speaker：Thomas Strobl (University of Lyon)

Time：2023年1月12日 20:00-21:00

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 Yang-Mills 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 16:00-17:00

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 right-symmetric 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) (ICT-UNIFESP)

Time：2022年12月15日 20:00-21:00

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 non-weakly 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 15:30-16:30

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 so-called 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 15:30-16:30

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 Harish-Chandra 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.

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 high-level academic papers in Comm. Math. Phys., Adv. Math., Trans. Amer. Math, Soc., Pro. Lond. Math. Soc., IMRN and other journals.

Quasi-local mass and geometry of scalar curvature

Speaker：Yuguang Shi (Peking Universtiy)

Time：2022年11月25日  10:30-11:30

Meeting ID：腾讯会议：520-112-012

Abstract：Let (Σ^(n-1),γ) be an (n-1)-dimensional orientable Riemannian manifold, H be a positive function on Σ^(n-1), 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 fill-in for the triple (Σ^(n-1),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  10:30-11:30

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 non-maximum 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 non-associative 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 Murray-von Neumann algebras

Speaker：Karimbergen Kudaybergenov (V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences)

Time：2022年11月18日  15:30-16:30

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 non-associative 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  15:45-16:45,

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 best-known 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 so-called “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  15:30-16:30

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 one-dimensional 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 well-known problems of algebraic topology and algebraic geometry, including the still open Milnor-Hirzebruch 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  15:30-16:30

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 well-known varieties of algebras. For example, they admit the Tits-Koecher-Kantor 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 Editor-in-Chief of Communications in Mathematics. His main area of research interest is in non-associative algebras.

Weak Leibniz algebras and transposed Poisson algebras

Speaker：Askar Jumadildayev (Kazakh-British Technical University）

Time：2022年10月28日  14:00-15:00 

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 two-sided 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 Kazakh-British Technical University. His research interests concern cohomologies and deformations of Lie algebras, N-commutators of vector fields, identities of non-associative algebras and operads theory.

SU-bordism: geometric representatives, operations, multiplications and projections

Speaker：Panov Taras (Moscow State University)

Time：2022年10月21日  15:00-16:00 

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 Conner-Floyd, Wall and Stong with the Adams-Novikov 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 SU-bordism has emerged, which is based on representing generators of the SU-bordism ring and other important SU-bordism classes by quasitoric manifolds and Calabi-Yau hypersurfaces in toric varieties.

We shall also discuss more specific topics related to SU-bordism. Namely we show that SU-linear operations in complex cobordism are generated by the well-known geometrical operations $\partial_i$. For the theory $W$ of $c_1$-spherical bordism, we describe SU-linear multiplications on W and projections $MU \to W$. We also analyse complex orientations on $W$ and prove results on the s-numbers 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 two-dimensional Jacobian conjecture

Speaker：Yucai Su （Tongji University）

Time：2022年10月14日  14:30-15:30 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 two-dimensional Jacobian conjecture in the speaker’s paper entitled ``a proof of 2-dimensional 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 2-dimensional 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 16:30-17:30 

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 n-operads 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

孤立波：1834-1984

Speaker：张大军 上海大学

Time：2022年09月23日 10:30-11:30 

Meeting ID：腾讯会议：309-266-962

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Fermi-Pasta-Ulam问题时发现并命名了“soliton” (孤立子), 两年以后Gardner-Greene-Kruskal-Miura 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(1834-1984)的历史，回顾期间(特别是1968-1984)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：869-2118-6000，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 mini-course, 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 K-theory and the coarse Baum-Connes conjecture involving the K-theory of Roe algebras.

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 sef-intersections set of Brownian motion. Professor Andrey will give students some time to understand the knowledge and give some small questions about the lecture.

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 10:30-11:30

Meeting ID：腾讯会议 ID：602-653-169

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 pp-waves 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 structures-a 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 higher-order 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 so-called L-infinity algebras, continuing with stacky groupoids, and closing with Lie n-groupoids. 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 10:30-11:30

Meeting ID：腾讯会议 ID：737-700-086

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、Bose-Einstein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 21:00-22:00

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 "quasi-derivations" 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 21:00-22:00

Meeting ID：腾讯会议 ID：939-656-494

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 10:00-11:00

Meeting ID：腾讯会议 ID：721-493-311                           

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 10:00-12: 00

Meeting ID：腾讯会议 ID：324-276-209

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 16:00-17: 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 16:00-18: 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.