Seminar in Mathematical Modeling and Analysis - Ludvig Svensson

The seminars in Mathematical Modeling and Analysis are aimed at researchers, employees, and students.

This week's seminar is given by Ludvig Svensson, Chalmers University of Technology and University of Gothenburg.

Abstract: Let $X$ be a reduced complex space of pure dimension. We consider divergent integrals of certain forms on $X$ that are singular along a subvariety defined by the zero set of a holomorphic section of some holomorphic vector bundle $E \rightarrow X$. We consider two different regularizations of such integrals, both depending on a choice of smooth Hermitian metric on $E$. Given such a choice, for each of the two regularizations there is a natural way to define a finite part of the divergent integral, and I will explain that they coincide. Furthermore, I'll present an explicit formula for the dependence on the choice of metric of the finite part, and briefly talk about how it was obtained.