Program
Introduction to Donaldson-Thomas invariants
Student No.:50
Time:Tue/Thu 8:00-9:50, 2017-05-16~ 2017-07-13 (No classes on public holidays)
Instructor:Yunfeng Jiang  [University of Kansas]
Place:Conference Room 1, floor 1, Jin Chun Yuan West Building
Starting Date:2017-5-16
Ending Date:2017-7-13

 

Description:


Inspired by string theory and gauge theory in physics, in recent years mathematical theories for the algebraic curve counting in algebraic varieties have been constructed, and have been proved to have deep connections to many branches of mathematics.  The most interesting theories include the Gromov-Witten theory, which is the curve counting theory via stable maps; and the Donaldson-Thomas theory, which is the curve counting theory via stable coherent sheaves.  These two theories have deep relationships. 
Not like the Gromov-Witten invariants, the Donaldson-Thomas invariants behave much like motivic invariants.  In this course I will introduce the original definition of Donaldson-Thomas invariants, and then explain why they have motivic properties by the work of Behrend. If time permits, we will go to the motivic Donaldson-Thomas invariants and their wall crossing properties.

 

 

Prerequisite:


Basic knowledge on Algebraic Geometry, and the knowledge of moduli spaces, especially the moduli space of stable sheaves.

 

 

Reference:

 

1. K. Behrend, Donaldson-Thomas invariants via microlocal geometry, Ann. Math., (2009).


2. R. Thomas, A holomorphic Casson invariants on Calabi-Yau threefolds and bundles on K3 fibrations, J. Diff. Geom. 54, 367-438, 2000. math.AG/9806111.


3. Y. Jiang, Note on MacPherson’s local Euler obstruction, preprint,  arXiv:1412.3720.