MAT 298: Seminars on Gromov-Witten Theory
Winter Quarter 2011. CRN = #30246
Fridays 4:10 - 5:00
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."