Events
7.13
7:30pm-9:30pm
Event Details:
Title:Summer Geometry & Physics Seminar
Date: July 13-18
Venue: Lecture Hall
Previous Seminars
| Date: | July 13, 7:30pm-9:30pm |
| Speaker: | Jiawei Zhou (YMSC) |
| Title: | On formality of some Boothby-Wang fibrations |
| Abstract: | 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. |
| Date: | July 14, 7:30pm-9:30pm |
| Speaker: | Ce Ji (Peking University) |
| Title: | Masur-Veech volumes and Siegel-Veech constants of moduli space of abelian differential: the minimal strata. |
| Abstract: | 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) |
| Date: | July 15, 7:30pm-9:30pm |
| Speaker: | Zhengping Gui (Tsinghua University) |
| Title: | W-algebra, topological vertex and affine Yangian |
| Abstract: | 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) |
| Date: | July 16, 7:30 pm-9:30 pm |
| Speaker: | Jingyi Xu (Peking University) |
| Title: | Localization in Gromov-Witten theory |
| Abstract: | 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. |
| Date: | July 17, 3:00 pm-5:00 pm |
| Speaker: | Zhengping Gui (Tsinghua University) |
| Title: | Geometry of localized effective theories, exact semi-classical approximation and the algebraic index |
| Abstract: | 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. |
| Date: | July 17, 7:30 am-9:30 am |
| Speaker: | Qingsheng Zhang (Peking University) |
| Title: | Landau-Ginzburg mirror symmetry. |
| Abstract: | 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. |
| Date: | July 18, 10:00 am-11:30 am |
| Speaker: | Xiaoxiao Yang (Tsinghua University) |
| Title: | Persistent Homology |
| Abstract: | 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. |
| Date: | July 18, 2:00 am-4:00 am |
| Speaker: | Chenglang Yang (Peking University) |
| Title: | Masur-Veech Volumes of Moduli Spaces of Holomorphic and Quadratic Differentials |
| Abstract: | 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). |
