Mathematical Methods from Physics

Date :From 2013-07-22 To 2013-09-05
Advisory committee :Shing-Tung Yau, Yan Soibelman, Nanhua Xi, Jie Xiao and Jiping Zhang
Local coordinators :Bangming Deng, Xiangmao Ding, Bo Feng, Fang Li (co-chair, contact person), Ke Wu (co-chair)
International coordinators :Li Guo, Zongzhu Lin (co-chair, contact person), Kefeng Liu (co-chair), Matilde Marcolli, Zhiwei Yun

This seven-week program includes several mathematical research areas that are closely related to mathematical physics, in particular to string theory and conformal field theory. Main topics of the program include integrable systems, mirror symmetry, geometric Langlands program, quiver varieties and quantum field theory, stability conditions and wall-crossing formulas. Some of these topics might appear to be purely mathematical and not related to one another. However, all these mathematical topics have a common physical connection--string theory.

Three objectives on this program

  • Bring together experts from different fields in order to communicate, to collaborate on common interests and to build further interactions among these different fields.
  • Increase interactions of researchers in China with those from other countries on these newly developed fields.
  • To expose junior researchers, in particularly postdocs and advanced graduate students, to the most advanced research topics. Emphasis will be put on learning the big pictures in order to understand the broad implications and interrelations among different research areas in China and among different fields of mathematics and physics.

Program Structure:

This seven-week program will consist of four workshops in addition to regular seminar talks by researchers in residence at KITPC. Each of the four workshops will focus on several relevant topics to highlight interactions among those topics and other research topics among participants who are in residence during/before/after the workshop. The topics of these workshops are

(1) Workshop 1: Non-commutative geometry, deformation theory and quantum groups.

Topics include quantum field theory, operads, Rota-Baxter algebras, and D-module theory, deformation theory, quantum groups, and non-commutative geometry. A-infinite algebras and A-infinite categories. Integrable systems and symplectic reductions.

(2) Workshop 2: Mirror symmetry and homological mirror symmetry.

Topics include sympletic geometry, Calabi-Yau manifolds and Calabi-Yau categories, A-infinite category, Fukaya category, Fourier-Mukaya transforms etc.

(3) Workshop 3: Donaldson-Thomes invariants and stability conditions.

Topics include representations of quivers and quiver variety, bridgeland stabiltity conditions, (algebraic, cohomological, and motivic) Hall algebras. Cluster algebras and cluster categories.

(4) Workshop 4: Langlands program and related representation

Topics include representations of algebraic groups and quantum groups, canonical basis, representations of Kac-moody groups, related geometric representation theory.

Sponsor:

Morningside Mathematical Center