课程 | 莫斯科国立大学教授开课通知
新学期选课你准备好了吗？北大数院特邀莫斯科国立大学数学力学系三位教授讲授为期三个月的本研课程，欢迎数院以及外院系的本科生和研究生选此课程，在增长数学知识的同时，体验全英式教学氛围，感受不同的教育理念。
Alexey Tuzhilin
Professor
Research Interests
Alexey Tuzhilin investigates Low-dimensional geometrical variational problems,including various generalizations of Steiner Problem on finding shortest networks(Steiner minimal trees). He pays special attention to one-dimensional minimal fillings in Gromov’s sense. In addition, he researches on the geometry of Gromov-Hausdorff space, i.e., the space of isometry classes of compact metric spaces. Alexey Tuzhilin obtained his many results in collaboration with Alexander O. Ivanov.
Course:
Geometry of Gromov-Hausdorff distance
Date:
Sep 9, 2019 - Dec 15, 2019
Time：
Wednesday 13:00 - 14:50
Friday 10:10 - 12:00
Place:
Room 206,Classroom Building No.2 (二教206)
Introduction：
This course is devoted to geometry of the Gromov-Hausdorff distance that measures difference between two metric spaces. If metric spaces are isometric then the distance vanishes, that is why it is naturally to consider the distance on isometry classes of metric spaces. In the case when the metric spaces in consideration are compact,this distance is a metric, and the corresponding hyperspace is called Gromov-Hausdorff space. The lectures mainly devoted to description of geometry of the Gromov-Hausdorff space.The convergence w.r.t. Gromov-Hausdorff distance has many beautiful applications. In particular, it was used by Gromov to prove that any discrete group with polynomial growth contains anilpotent subgroup of nite index. This distance has been applied in computer graphics and computational geometry to find correspondences between different shapes. In Cosmology,Gromov-Hausdorff distance was used to prove stability of the Friedmann model.
Alexander Zheglov
Associate Professor
Research Interests
Algebraic geometry, algebraic number theory, integrable systems, higher local elds,valuation theory.
Course:
Algebra, Geometry and Analysis of Commuting Differential Operators
Date:
Sep 9, 2019 - Dec 15, 2019
Time：
Tuesday 13:00 - 14:50
Thursday 15:10 - 17:00
Place:
Room 503, Classroom Building No.3(三教503)
Introduction：
This course involves an explanation of basic ideas and constructions from the theory of commuting ordinary differential operators as well as an overview of related open problems from algebra, algebraic geometry and complex analysis. One of the objectives of the course is topropose new tasks for research. It is highly recommended to be familiar with the basic topics from Algebra and Commutative algebra (though all auxiliary results from these topics will be reminded as necessary)
Georgy Sharygin
Associate Professor
Research Interests
Poisson geometry and integrable systems, invariats of Poisson and symplectic manifolds,
Quantum Groups and Galois-type Extensions, (Hopf-type) Cyclic (co)homology with coefficients and its applications, Geometry and Topology of Loop Spaces, K-theory and its applications, higher homotopy structures in cyclic homology and geometry, characteristic classes of simplicial and homological manifolds.
Course:
Deformation quantization
Date:
Sep 23, 2019 - Dec 20 , 2019
Time：
Monday 18:40 - 20:30
Wednesday 18:40 - 20:30
Place:
Room 405, Classroom Building No.3 (三教405)
Introduction：
The purpose of this course is to give a concise introduction into the wide circle of problems, centered at the deformation quantization program and its applications. We shall begin with the classical constructions of Weyl and Moyal, give a detailed account of the symplectic deformation quantization constructions, due to Gutt, Lecomte and de Wilde, and to Fedosov. The course will culminate at the celebrated Kontsevich's deformation quantiza-tion theorem. I will try to give two proofs thereof: the original one, due to Kontsevich, and Tamarkin's proof, based on the homological theory of oper-ads. If time permits, I will describe some other applications of the theory we develop, like algebraic index theorem of Fedosov, Nest and Tsygan, or the proof of Deligne's conjecture.
🕓 Course Schedule