Program
Geometry and Physics Seminar
Student No.:40
Time:Tue 13:30-15:00, Oct.9-Jan.15
Instructor:Li Si, Zong Zhengyu, Zhou Jie, Tang Xinxing  
Place:Jing Zhai 105
Starting Date:2018-8-28
Ending Date:2019-1-15

2018-10-16 Tuesday

Speaker: Shuai Guo(Peking University)

Title: BCOV's Feynman graph sum formula via NMSP


Abstract:
I will talk about the physics and mathematics approaches to the Gromov-Witten invariants of quintic 3-fold, and how they are related via the language of R-matrix action on CohFT. This is a joint work with H-L Chang and Jun Li.



2018-10-08 Monday

Speaker: Alfredo Najera

Title: Toric degenerations of cluster varieties, cluster duality and mirror symmetry


Abstract:
Cluster varieties are a special kind of lof-Calabi-Yau varieties. They come in pairs (A,X), with A and X built gluing dual tori via cluster transformations. Partial compactifications of A-varities and their toric degenerations have been studied extensively by Gross, Hacking, Keel, and Kontsevich (GHKK). These partial compactifications generalize the polytope construction of toric varieties, a construction which is recovered in the toric central fiber of the degeneration.

In this talk we introduce the notion of X-cluster varieties with coefficients. We use this notion to construct partial compactifications of an arbitrary X-cluster variety. Moreover, we use it to construct a flat degenerations of any specially completed X-cluster variety (in the sense of Fock-Goncharov) to the toric variety associated to its cluster complex. Our construction generalizes the fan construction of toric varieties. We further show that our degeneration is cluster dual to GHKK's toric degeneration of A-cluster varieties. If time permits we will outline two applications:

1) We can show that the toric degeneration of the Grassmannian Gr_k(C^n) constructed by Rietsch-Williams in 2017 coincides with GHKK's toric degeneration.

2) We can use our approach to give a precise relation of cluster duality and Batyrev-Borisov duality of Gorensteintoric Fanos in the context of mirror symmetry.

This is based on joint work with Lara Bossinger, Juan Bosco Frias Medina, and Timothy Magee, and if we have time to address the Batyrev-Borisov connection, Man-Wai Cheung as well.



2018-8-28 Tuesday

Speaker: Gao Honghao

Title: Augmentations and Sheaves for Knot Conormals

Abstract: Knot invariants can be defined using Legendrian isotopy invariants of the knot conormal. There are two types of invariants raised in this way: one is the Chekanov-Eliashberg differential graded algebra together with augmentations associated to this dga, and the other one is the category of simple sheaves microsupported along the knot conormal. Nadler-Zaslow's theorem suggests a connection between the two types of invariants. In this talk, I will manifest the correspondence explicitly.


History:
Spring, 2018: http://ymsc.tsinghua.edu.cn/sjcontent.asp?id=1064
2017: http://ymsc.tsinghua.edu.cn/sjcontent.asp?id=921
Autumn, 2016: http://ymsc.tsinghua.edu.cn/sjcontent.asp?id=860
Spring, 2016: http://ymsc.tsinghua.edu.cn/sjcontent.asp?id=799
Autumn, 2015: http://ymsc.tsinghua.edu.cn/sjcontent.asp?id=731