您现在的位置: 首页» 通知公告

通知公告

2022年秋季学期俄罗斯专家新开设四门课程上课时间和上课方式通知(9月5日开课)

Representation Theory

 

Lecturer:Evgeny Smirnov - Higher School of Economics 

Abstract: Representation Theory studies abstract algebraic structures, such as groups or rings, by representing their elements as linear transformations of vector spaces. It is a fundamental tool to study groups, algebras and their actions using linear algebra.
Representation Theory plays an important role in many recent developments of mathematics and theoretical physics. In our course we introduce basic concepts and results of the classical theories of complex representations of finite groups, Lie groups and Lie algebras.
The course consists of three parts. The first part is devoted to representation theory of finite groups; we will use this example to get acquainted with the fundamental concepts of the theory, to be generalized later. In the second part, we will discuss the representation theory of algebras in general and then study in detail the so-called path algebras of quivers and apply this to problems of linear algebra. In the final part, we study representations of Lie groups and Lie algebras.

Time:Mondays     15:10-17:00

           Thursdays    18:40-20:30

Join Zoom Meeting:

https://us02web.zoom.us/j/6687697417?pwd=aCszVjJ6YlBDRmJBdE5SVTJydWF1UT09

Meeting ID:668 769 7417

Password:123451

Teaching Assistant Contact

Email: 2001110016@pku.edu.cn 

Recording: https://disk.pku.edu.cn:443/link/EFB541F8F4E3C0D5723B713D7F4BECCE

结课时间:12月5日周一 15:10-17:00

 

 

 

Geometry, Quantization and Semi-Classical Asymptotics

 

Lecturer:Andrei Shafarevich Lomonosov Moscow State University

Abstract: The main goal of the course is to present geometric and analytical ideas related to semi-classical theory, the theory of quantization of isotropic manifolds, as well as with description of singularities for PDE’s.

Contents.

Week 1. Symplectic manifolds and classical mechanics. Hamiltonian systems.

Week 2. Integrable systems.

Week 3. Quantization of classical systems. Dirac quantization.

Week 4. Pseudo-differential operators. Weyl symbolds.

Week 5. Sobolev spaces and pseudo-differential operators.

Week 6. Geometric quantization.

Week 7. Semi-classical asymptotics. Quantization of Lagrangian manifolds.

Week 8. Maslov canonical operator. Maslov class and Maslov index.

Week 9.  Quantization of complex vector bundles over isotropic manifolds.

Week 10. Semi-classical quantization and Morse theory.

Week 11. Propagation of singularities for hyperbolic systems.

Week 12.  Lagrangian manifolds and Fourier integral operators. Wave fronts.

Time:Mondays    18:40-20:30

            Tuesdays    18:40-20:30

Join Zoom Meeting:

https://us02web.zoom.us/j/6997780703?pwd=eU9abGY3TytSZDlwd09lZzlLRVY0UT09

Meeting ID:699 778 0703

Password:8242931

Teaching Assistant Contact

Email:1321088183@qq.com

Recording: https://disk.pku.edu.cn/link/30079CEEE3C16FACA04FA4B3AFF28F80

结课时间:11月29日(周二)18:40-20:30

 

课程调整一次:

时间:周四(2022.11.17)18:30-20:30

参课方式:腾讯会议

Meeting number: 266-701-382

Pass code: 824293

Link: https://meeting.tencent.com/dm/dMGqGrd876xA

 

Fundamentals of Calculus of Variations and Optimal Control

 

Lecturer:Eugene Stepanov  - Higher School of Economics

Abstract: The course is an introduction to the modern calculus of variations and its basic tools with an emphasis on concrete problems of variational nature, both classical and modern ones. Among the problems treated, there will be some shape optimization problems, classical mechanics, isoperimetric problems, existence and uniqueness of solutions to some PDEs of variational nature and  optimal control problems. 

Time:Tuesdays    13:00-14:50

            Fridays       13:00-14:50

Join Zoom Meeting:

https://us02web.zoom.us/j/6687697417?pwd=aCszVjJ6YlBDRmJBdE5SVTJydWF1UT09

Meeting ID:668 769 7417

Password:123451

Teaching Assistant Contact

Email 1321088183@qq.com         

Recordinghttps://disk.pku.edu.cn/link/A53751624FFCEA62F28D7FC1726FE168

结课时间:11月25日(周五 ) 13:00-14:50

 

Geometry and Topology of nilmanifolds

 

Lecturer:Dmitry Millionshchikov - Lomonosov Moscow State University

 

Abstract: Homogeneous spaces play an important role in the apparatus of modern fundamental and applied mathematics and theoretical physics. The concept of symmetry brings together geometry, topology, algebra and analysis. This course is devoted to such an important subclass of homogeneous spaces as nilmanifolds, i.e. homogeneous spaces of nilpotent groups. The study and application of nilmanifolds and invariant geometric structures (Riemannian and pseudo-Riemannian metrics, complex, hypercomplex, symplectic and affine structures) has experienced rapid development in recent decades. This course is intended to be an introduction to this rapidly developing field, located at the intersection of different mathematical sciences. On the other hand, using the example of nilmanifolds, we will touch upon such important sections of topology as the theory of invariant de Rham cohomology, study Massey products and the concept of formality, and establish its connection with symplectic and Kähler structures. The second part of the course will be devoted to the study of left-invariant geometric structures on nilmanifolds, in particular, we will discuss invariant nilsoliton metrics. We will try to skip the technically complicated proofs, focusing on the most important examples, ideas and basic geometric constructions.

Time:Wednesdays    18:40-20:30

             Fridays            18:40-20:30

Join Zoom Meeting

https://us02web.zoom.us/j/6997780703?pwd=eU9abGY3TytSZDlwd09lZzlLRVY0UT09

Meeting ID:699 778 0703

Password:8242931

Teaching Assistant Contact

Email:dszzy@pku.edu.cn                                        

Recording: https://disk.pku.edu.cn:443/link/4F5E9CCC9BD5FC09CCA74A8BDB30CED9

结课时间:11月30日周三18:40-20:30

TOP