题目：Newton Polyhedrons and Hodge Numbers of Non-degenerate Laurent Polynomials

报告人: 王浩旭 博士（清华大学丘成桐数学中心）

摘要: 

Claude Sabbah has defined the Fourier transform G of the Gauss-Manin system for a nondegenerate and convenient Laurent polynomial and has shown that there exists a polarized mixed Hodge structure on the vanishing cycle of G.

In this talk, we consider certain non-degenerate and convenient Laurent polynomials, whose Newton polyhedron at infinity is a simplicial polytope P. First, we consider the stacky fan given by P and show that for each quotient stacky fan, there is a natural polarized mixed Hodge structure on the ring of conewise polynomial functions on it. Then, we describe the polarized mixed Hodge structure on the vanishing cycle associated to stacky fan using these rings of conewise polynomial functions. In particular, we compute the Hodge diamond of the vanishing cycle. As a further consequence, we can solve the Birkhoff problem of such a Laurent polynomial by using elementary methods.

报告时间：2024年6月18日（周二）上午10:00-11:00

报告地点：教二楼 627

联系人：方江学