NCTS Seminar in Algebraic Geometry

-- A Winter Short Course in Gromov-Witten Theory --
Speaker : Prof. Yuan-Pin Lee  §õ¤¸Ùy  (University of Utah)

Date

Time

 Topic

Dec. 29, 2003  (Monday)

13:00 - 14:10

 Introduction to tautological rings

Jan. 5, 2004  (Monday)

14:00 - 15:10

 Relations in tautological rings and its applications

Jan. 14, 2004  (Wednesday)

10:30

 Loop groups in Gromov-Witten theory

Jan. 16, 2004  (Friday)

10:30

 Invariance of tautological rings and GW theory

Abstract:

1.This is an introductory talk to the subject of the tautological rings.  Tautological rings are subrings of Chow rings of moduli spaces of curves. They are introduced by Mumford for their many good (conjectural) properties. Some of the properties will be discussed.

2.The discussion of the tautological rings is continued, with the emphasis on the relations of tautological cycles and its applications to enumerative geometry.


3.The main theme of this talk is to introduce Givental's framework of formal semisimple Frobenius manifolds and how the loop groups arise in this framework.


4.Combining the previous 3 lectures, we will see how tautological rings are applied to the study of Gromov-Witten theory. In particular, Virasoro conjecture for semisimple Frobenius manifolds will be proved up to genus two.


Place: Lecture Room B of NCTS,
           4th Floor, The 3rd General Building, National Tsing Hua University.

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