学术活动

7.13

19:30-21:30

Event Details:

Title: 暑期数学物理讨论班

时间: 7月13日-18日,周二到周五晚上7:30。周六周日早上10点,下午3点,晚7:30。

场地:数学高等研究院报告厅

已举办的研讨会:

时间:7月13日,7:30 pm - 9:30 pm
主讲人:周嘉伟(YMSC)
题目On formality of some Boothby-Wang fibrations
摘要:A Boothby-Wang fibration is a circle bundle over a symplectic manifold whose curvature is the symplectic form. When the base is a formal manifold, the circle bundle is not necessarily formal. Suppose the base satisfies hard Lefschetz property. We explore the condition that makes the circle bundle also formal.
时间:7月14日,7:30 pm - 9:30 pm
主讲人:季策(北京大学)
题目:Masur-Veech volumes and Siegel-Veech constants of moduli space of abelian differential: the minimal strata.
摘要:The Masur-Veech volumes and Siegel-Veech constants are numerical invariants defiened on strata of abelian differentials. In recent years the method intepreting those invariants to intersection numbers on the moduli space has been established. In this talk we will give a brief review of the definition of these invariants and introduce the proof computing the Masur-Veech volume of minimal strata of abelian differential to be an intersection number. This talk is a review based on the work of A. Sauvaget (https://arxiv.org/abs/1801.01744)
时间:7月15日,7:30 pm - 9:30 pm
主讲人:桂政平(清华大学)
题目:W-algebra, topological vertex and affine Yangian
摘要:I will review the nolinear chiral algebra W_{1+\infty} and its connection to the affine Yangian. The characters of completely degenerate representations of W_{1+\infty} are given by the topological vertex. Many properties that are difficult to study in the W_{1+\infty} picture turn out to have a simple combinatorial interpretation, once translated to the Yangian picture. This talk is a review based on the work of Tomas Prochazka(arXiv:1512.07178v2)
时间:7月16日,7:30 pm - 9:30 pm
主讲人:许景毅(北京大学)
题目:Localization in Gromov-Witten theory
摘要:Localization is a technique for computing Gromov-Witten invariants of spaces with torus action whose fixed points and one-dimensional orbits are isolated. We will briefly review the torus localization on the moduli space of stable maps to the projective space P^m, and then obtain a Birkhoff factorization of the S-matrix. An example of the projective line will be given.
时间:7月17日,3:00 pm - 5:00 pm
主讲人:桂政平(清华大学)
题目:

Geometry of localized effective theories, exact semi-classical approximation and the algebraic index

摘要:In this talk we describe a general mathematical framework to study the quantum geometry of sigma-models when they are effectively localized to small fluctuations around constant maps. We illustrate how to turn the physics idea of exact semi-classical approximation into a geometric set-up in this framework, using Gauss-Manin connection. This leads to a theory of “counting constant maps” in a nontrivial way.  We explain this program by a concrete example of topological quantum mechanics and show how “counting constant loops”  leads to a simple proof of the algebraic index theorem. This talk is based on a joint work with Si Li and Kai Xu.


时间:7月17日,7:30 pm - 9:30 pm
主讲人:张庆生 (北京大学)
题目:Landau-Ginzburg mirror symmetry.
摘要:Landau-Ginzburg mirror symmetry describes the equivalence between FJRW theory (LG A-model) of an invertible polynomial and Saito-Givental theory (LG B-model) of the mirror polynomial. The establishment of LG mirror theorem for the polynomial with small central charge is due to the work of many mathematicians, and a general mirror theorem has been proved by He-Li-Shen-Webb. I will review their work and introduce an understanding of the mirror theorem from the viewpoint of Giental’s Lagrangian cone. This talk is based on the work of He-Li-Shen-Webb (https://arxiv.org/abs/1503.01757 ) and some discussions with Guo.
时间:7月18日,10:00 pm - 11:30 pm
主讲人:杨潇枭 (清华大学)
题目:Persistent Homology
摘要: Persistent homology is a method in topological data analysis. In this talk, I will introduce the motivation and definition of persistent homology, then I will introduce the barcode and give some examples.
时间:7月18日,2:00 pm - 4:00 pm
主讲人:杨成浪 (北京大学)
题目:Masur-Veech Volumes of Moduli Spaces of Holomorphic and Quadratic Differentials
摘要:The Masur-Veech volumes are important invariants of moduli spaces of differentials, which connect dynamics, algebraic geometry, combinatorics, etc. In this talk, I will introduce a method calculating those volumes. They are developed by Eskin and Okounkov (arXiv: 0006171, 0505545).


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