D-modules, motivic integrals and hypersurface singularities
Apr
06
2023
Speaker : 2:00PM Wu Lei
Time : 14:00
Location :
Title: D-modules, motivic integrals and hypersurface singularities
Speaker: Wu Lei(Tenured Associate Professor of School of Mathematics, Zhejiang University)
Time: 2023-04-06, 14:00-15:00
Location: 210, Building 2, Hainayuan, School of Mathematical Sciences, Zijingang Campus.
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.