Title: D-modules, index theorems and topology
Speaker: Lei Wu
Speaker Info: University of Utah
In classical differential geometry, the Chern-Gauss-Bonnet theorem provides a beautiful index formula connecting geometry to topology. In the first half of this talk, I will discuss how it can be generalized to all perverse sheaves on projective manifolds using D-modules, which is the Dubson-Kashiwara index formula. Then I will talk about generalizations of the Dubson-Kashiwara index formula for perverse sheaves on quasi-projective manifolds from a logarithmic point of view, and how they are related to Grothendieck-Riemann-Roch using intersection theory. This is based on joint work with Peng Zhou.Date: Thursday, October 24, 2019
In the second half of the talk, I will describe a similar story but from a relative perspective. The topology of Milnor fibers associated to a holomorphic function f contains information on the singularities of f. Using D-modules, one can construct the Bernstein-Sato polynomial for f. By a classical theorem of Kashiwara-Malgrange, the monodromy eigenvalues of Milnor fibers can be calculated by using roots of the Bernstein-Sato polynomial. I will talk about how this can be generalized for several holomorphic functions by using Alexander modules in the sense of Sabbah and Bernstein-Sato ideals. This is based on work joint with Nero Budur, Robin Veer and Peng Zhou.