DMM seminar

Speaker: Huai-Liang Chang (HKUST)
Title: Introduction to Gromov Witten and Fan-Jarvis-Ruan-Witten theory
Date (JST): Mon, Jun 18, 2012, 14:00 - 17:00
Place: Seminar Room A
Related File: 716.pdf
Abstract: 14.00 to 15.00
Title: Introduction to Gromov Witten and Fan-Jarvis-Ruan-Witten theory

Gromov-Witten (GW) theory counts Riemann surfaces in a complex manifold.
It originates from topological string theory and becomes a branch in symplectic geometry. Later Li-Tian and Behrend-Fantechi gave an algebro-geometric construction.
When the complex manifold is substituted by a Landau Ginzburg space (X,W), the physical and symplectic approach perturb "Witten equation" to define the analogous invariants. We will discuss the above and also the problem about hyperplane property for higher genus GW of Quintic threefold.
15.30 to 17.00

Title: Algebro geometric construction of A twisted Landau Ginzburg theory

For affine Landau Ginzburg space (X,W), Fan-Jarvis-Ruan(-Witten) defines curve enumeration invariants in symplectic geometry. A genus zero case where X=K_P4 is treated by Guffin & Sharpe (-Witten) by path-integral.

Apply SUSY-variation to the superpotential W we obtains a "cosection".
Then "Kiem-Li cosection localization" provides an algebro-geometric construction of FJRW theory. Our procedure applied to the moduli space of maps with "p-field" gives algebro-geometric construction of K_P4's LG-model for all genus and generalize Kontseviech's hyperplane property to all genus.
As a byproduct we get an algebro-geometric proof of "separation of GW contributions" in g=1 Li-Zinger Conjecture.
Remarks: Break 15:00-15:30