Workshop on Geometry and Physics IV, 2018

Purpose:

This workshop consists of a few conference talks, aiming to bring together researchers to communicate on recent progress in algebraic/symplectic geometry, mathematical physics and related topics. It is a continuation of exploring a good way to bring potential collaborations among the participants. 

Organizers:

HU, Jianxun  (Sun Yat-sen University)
LI, Changzheng (Sun Yat-sen University)

Speakers:

  LEUNG, Naichung Conan  (The Chinese University of Hong Kong)

  SHEN, Junliang      (ETH Zurich)

  WU, Weiwei        (University of Georgia)

Program:

Venue: Room 415 (New Math. Building)

Title and Abstracts:

SYZ mirror symmetry (I) and (II) (by N.C. Leung)
Abstract: In this talk, we will discuss various problems in Strominger-Yau-Zaslow (SYZ) mirror symmetry, which is one of the main approaches in the study of mirror symmetry.
　

Chow groups, derived categories, and K3 surfaces (I) and (II) (by J. Shen)
Abstract: After a brief review of Chow groups and derived categories of algebraic varieties, we will focus on recent progress on the study of these structures for K3 surfaces. In particular, we will discuss the interplay between algebraic cycles and coherent sheaves on projective K3 surfaces, which includes the work of Beauville-Voisin, Huybrechts, O'Grady, Voisin, and the joint work with Qizheng Yin and Xiaolei Zhao. Then we will further discuss their generalizations to non-commutative K3 categories and potential connections to mirror symmetry.

Title 1: Introduction to Lagrangian correspondence (by W. Wu)                                          
Abstract: I will quickly go through the notion of generalized Lagrangians, geometric compositions, and how to define Floer cohomology for them. Easy examples will be given, and a naive comparison with Fourier-Mukai functors is presented. I will also discuss some technical problems when we apply this technique.

Title 2: Introduction to Lagrangan cobordism (by W. Wu)                                          
Abstract: The talk will survey the Lagrangian cobordism theory in Biran-Cornea's sense. Such Lagrangian cobordism will give mapping cones between objects in Fukaya categories. I will also explain the relation between Lagrangian cobordisms and Lagrangian surgeries, as well as the computation of connecting maps. During the talk, some discussions about correspondence between connecting maps (of distinguished triangles) in Fukaya categories and in derived categories will take place.

Accommodations and Local information:

Hotels on campus:
　

SYSU hotel & Conference Center（中山大学学人馆）

Address: North gate of Sun Yat-sen University, Binjiang Dong Road, Haizhu District, Guangzhou
Tel: 020-89222888                 Website: http://www.syskaifeng.com

Contact information:

Ms. YU, Jinyun 
Email: yujin250 AT 163.com 

Prof. LI, Changzheng 
Email: lichangzh AT mail.sysu.edu.cn

Phone: +86-20-84111738 
School of Mathematics, Sun Yat-sen University, No. 135, Xingang Xi Road, Haizhu, Guangzhou, 510275, China