主 题: The Fifth Advanced Seminar in Symplectic Geometry and Topological Field Theory
报告人: Felix Janda (IMJ-PRG), Jake Solomon (Hebrew University), Sara Tukachinsky (Hebrew University) ()
时 间: 2016-05-16 9:00 - 16:00
地 点: 甲乙丙报告厅
Schedule:
Mon (5/16) to Fri (5/20)
Mon, Tue, Wed morning 9-11: Jake Solomon
Thu, Fri morning 9-11: Sara Takachinsky
Mon, Tue, Wed, Fri afternoon 2-4: Felix Janda
There is a 10-min break at the middle of each session (up to the speaker).
Titles & Abstracts:
1. Felix Janda
Title:
Tautological relations on the moduli space of curves
Abstract:
The tautological ring is a subring of the Chow (or cohomology) ring of the moduli space of curves containing many natural geometric classes. There is a canonical set of generators of the tautological ring, and the relations between the generators are called tautological relations.
In these series of lectures we first review the definition and the basic properties of the tautological ring of the moduli space of stable curves. We then proceed to review conjectures about the structure of the tautological ring and methods of producing tautological relations. The notion of a cohomological field theory with its applications to the recent advances in the study of tautological relations will play a central role in the lectures. In the end we will discuss recent work (joint with E. Clader) on tautological relations related to the double ramification cycle.
2. Jake Solomon
Title:
Stable disks, open KdV and Virasoro
Abstract:
I will discuss intersection theory on the moduli space of stable marked disks and how it leads to the open KdV hierarchy and the open Virasoro constraints. Canonical boundary conditions will be constructed that give rise to well-defined open descendent integrals. Hands-on examples will be presented. The open descendent integrals will be shown to satisfy the open string, dilaton and TRR equations. These equations allow the computation of all genus zero descendent integrals, motivating the definition of open KdV and Virasoro.
These talks are based on joint work with R. Pandharipande and R. Tessler.
3. Sara Tukachinsky
Title:
Point-like bounding chains and OGW theory
Abstract:
The goal of the talks is to define genus zero open Gromov-Witten invariants in arbitrary dimension. These invariants count stable disk maps with Lagrangian boundary conditions.
Following the approach of Fukaya et al., we will give A_\infty structures to the ring of differential forms on a Lagrangian submanifold. Then we define bounding chains and a natural equivalence relation on them. We give a canonical parametrization of the space of equivalence classes of chains. Next we show that the superpotential gives rise to a well-defined function on equivalence classes of bounding chains. This function is the generating function of genus zero open Gromov-Witten invariants.
This is joint work with Jake Solomon.
Organizers:
Huijun Fan, Peking University
Bohan Fang, Peking University
Gang Tian, Peking University
Xiaobo Liu, Peking University
2016 Workshop on Symplectic Geometry and Mathematical Physics
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Date:
May 23-27, 2016
Venue:
Lecture Hall, Jia Yi Bing Building, 82 Jing Chun Yuan, BICMR
北京大学镜春园82号甲乙丙楼二层报告厅
Directions to BICMR
Organizing Committee:
Huijun Fan, Peking University
Bohan Fang, Peking University
Shuai Guo, Peking University
Xiaobo Liu, Peking University
Scientific Committee:
Anmin Li, Sichuan University
Xiaobo Liu, Peking University
Yiming Long, Nankai University
Yongbin Ruan, Peking Unversity
Gang Tian, Peking University
Sponsors:
National Natural Science Foundation of China
Beijing International Center For Mathematical Research, Peking University
Confirmed Speakers:
Mohammed Abouzaid, Columbia University
Alejandro Adem, University of British Columbia
Alexandr Buryak, ETH Zurich
Kwokwai Chan, Chinese University of Hong Kong
Penka Georgieva, IMJ-PRG
Hai-Long Her, Nanjing Normal University
Jianxun Hu, Sun Yat-Sen University
Felix Janda, IMJ-PRG
Timothy Perutz, University of Texas at Austin
Brad Safnuk, Central Michigan University
Shanzhong Sun, Capital Normal University
Ran Tessler, Hebrew University
Hsiang-hua Tseng, Ohio State University
Kazushi Ueda, University of Tokyo
Bai-Ling Wang, Australian National University
Gehao Wang, Peking University
Guangbo Xu, Princeton University
Zhengyu Zong, Tsinghua University
Schedule:
5.23
Monday morning
Adem 9:30-10:30
Janda 10:45-11:45
Monday afternoon
Safnuk 2:00-3:00
Buryak 3:30-4:30
5.24
Tuesday morning
Hu 9:30-10:30
Tessler 10:45-11:45
Tuesday afternoon
Zong 2:00-3:00
Ueda 3:15-4:15
Gehao Wang 4:30-5:30
5.25
Wednesday morning
Tseng 9:30-10:30
Chan 10:45-11:45
5.26
Thursday morning
Abouzaid 9:30-10:30
Perutz 10:45-11:45
Thurday afternoon
Sun 2:00-3:00
Georgieva 3:15-4:15
He 4:30-5:30
5.27
Friday morning
Bai-Ling Wang 9:30-10:30
Xu 10:45-11:45
Accommodation and Travel Information:
BICMR will accommodate all speakers and invited participants in “Zhong Guan Xin Yuan” Hotel. By default, rooms have been booked for the arrival on May 22 and departure on May 28. The hotel is across the street of Peking University Campus, about 10-15 minutes’ walk to BICMR. If you plan to have an extended stay, please inform Yiwei Li (liyiwei@pku.edu.cn) so that we can make proper arrangements.
Other participants are responsible for arranging and paying for their own reservations for hotel accommodations.
Hotel Address:
“Zhong Guan Xin Yuan” Hotel (Zhongguanyuan Global Village)
No. 216 Zhongguancun North Road, Haidian District, Beijing 100871, China
Map: From Airport to “Zhong Guan Xin Yuan” Hotel
PKU campus map
Website: www.pkugv.com
Tel: + (86 10) 62752288
Fax: + (86 10) 62752236
Registration:
There will be no registration fee. Please register through this link at your earliest convenience so that we can make proper arrangement for the workshop.
Contact:
Bohan Fang
Email bohanfang@gmail.com
Yiwei Li
Email liyiwei@pku.edu.cn
