D-modules, motivic integrals and hypersurface singularities
代数几何与辛几何系列学术报告
Title: D-modules, motivic integrals and hypersurface singularities
报告人：吴磊 （浙江大学数学学院 长聘副教授）
地点：浙大紫金港校区海纳苑2幢210
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.