Speaker: Prof. Huijun Fan (范辉军教授）

Time: 14:30-15:30, 22 December, 2023 (Friday) (Beijing time)

Venue: 华信书院，CC126

Abstract

An LG model (M, is given by a noncompact complex manifold M and the holomorphic function f defined on it, which is an important model in string theory. Because of the mirror symmetry conjecture, the research on the geometric structure and quantization theory of LG model has attracted more and more attention. Given a Calabi Yau (CY) manifold, we can define Gromov Witten theory (A theory) on it, and also study the variation of Hodge structure on its mirror manifold (B theory). Accordingly, LG model includes A theory FJRW theory and Hodge structure variational theory.

This report starts with some examples, gives the geometric and topological information contained by a LG model, and derives the relevant Witten equation (nonlinear) and Schrodinger equation (linear). The study of the solution space of these two sets of equations will lead to differen t quantization theories. Secondly, we give our recent correspondence theorem of Hodge structures between LG model and CY manifold. Finally, we will discuss some relevant issues.

About Prof. Fan

Huijun Fan is the director of the Key Laboratory of Mathematics and Applied Mathematics of the Ministry of Education of Peking University and the deputy director of the Sino Russian Math Center. His res earch direction is geometry and mathematical ph ysics , concentrating on problems arising from mirror symmetry.