**MAT 298: Seminars on Gromov-Witten Theory**

Winter Quarter 2011. CRN = #30246

Fridays 4:10 - 5:00

3106 MSB

Organizer: Motohico Mulase

This term we meet on Fridays 4:10 to 5:00.

**
January 7. Michael Kapovich:
**
"Remarks on the character variety of a knot complement and the
volume conjecture."

** January 14.
Motohico Mulase:** "The Eynard-Orantin Theory in
Geometry -- A Mystery from Physics."

This talk is planned to be an introduction.

** January 21.
Jerry Kaminker:** "Volume of character varieties and
localization, I."

** January 28.
Jerry Kaminker:** "Volume of character varieties and
localization, II."

** January 31.
Jian Zhou, Tsinghua University:** "Local mirror curves and
holomorphic disc invariants."

This talk is given in the Geometry/Topology Seminar.

According to a conjecture of Hori-Iqbal-Vafa, the mirror geometry of a toric Calabi-Yau 3-fold is encoded in a local mirror curve determined by the toric data. A conjecture of Aganagic-Vafa claims that the locla mirror curve can also be determined from the holomorphic disc invariants of toric 3-fold. Finally a conjecture by Lerche-Mayr states the holomorphic disc invariants can be determined by a generalized Picard-Fuchs system. In this talk we will explain these conjectures and the verifications of some important special cases.

Professor Zhou will give us several introductory talks on Gromov-Witten theory, topological vertex, and related topics during his stay in Davis.

** February 2. (Irregular time and date: 3:10, in MSB 2112)
Jian Zhou, Tsinghua University:** "Introduction to Gromov-Witten theory."

This is a down to earth introduction to the theory using a simple example. Explanations will be given for the Picard-Fuchs equation, mirror symmetry, and "A-model" GW invariants.

** February 4.
Jian Zhou, Tsinghua University:** "Geometry
of Calabi-Yau spaces and the BKMP conjecture, I --
Representation theory and Hodge integrals."

** February 7. (Irregular Time, Monday
3:10 - 5:30 in 3240)
Jian Zhou, Tsinghua University:**
"Representation theory, Burnside formula,
and the Marino-Vafa formula."

** February 9. (String Theory Seminar, Wednesday,
3:10 at 2110)
Jian Zhou, Tsinghua University:**
"Integrality properties of local mirror maps."

Abstract: I will discuss various results and conjectures related to the integrality properties of local mirror maps.

** February 11.
Jian Zhou, Tsinghua University:** "Geometry
of Calabi-Yau spaces and the BKMP conjecture, II --
A new derivation of the Eynard-Orantin topological recursion."

** February 18.
Jerry Kaminker:** "Group valued moment maps and the Meinrenken reduction, I."

** February 25.
Jerry Kaminker:** "Group valued moment maps and the Meinrenken reduction, II."

** March 4.
Olivia Dumitrescu:** "Atiyah-Bott Localization - Introduction and Examples, I."

** March 11.
Olivia Dumitrescu:** "Atiyah-Bott Localization - Introduction and Examples, II."