Back to Algebraic Geometry Seminar: Spring 2023
Algebraic Geometry Seminar
Date: Tuesday, May 2, 2023
Time: 3:30PM - 4:30PM
Location: LCB 323
Lei Wu
Zhejiang University
Title |
D-modules, motivic integrals and hypersurface singularities |
Abstract |
This talk is an invitation to the study of monodromy conjecture for hypersurfaces in complex affine spaces. I will recall two different ways to understand singularities of hypersurfaces in complex affine spaces. The first one is to use D-modules to define the b-function (also known as the Bernstein-Sato polynomial) of a polynomial (defining the hypersurface). The other one uses motivic integrals and resolution of singularities to obtain the motivic/topological zeta function of the hypersurface. The monodromy conjecture predicts that these two ways of understanding hypersurface singularities are related. Then I will discuss some known cases of the conjecture for hyperplane arrangements. There will be plenty of examples. |
Algebraic Geometry