Abstract for the talk on 14.06.2023 (13:30 h)

Seminar on Nonlinear Algebra

Christopher Voll (Universität Bielefeld)
Counting with p-adic integrals
14.06.2023, 13:30 h, MPI für Mathematik in den Naturwissenschaften Leipzig, G3 10 (Lecture hall)

Suppose we are given a multivariate polynomial over the integers. What can be said about the zeros of this polynomial modulo a natural number N? As I will explain, considering this question for all natural numbers simultaneously leads to a data set with remarkable structure and symmetry.

One route to appreciate this hidden information goes via p-adic integration. I will illustrate this approach – hands-on and from scratch – on a few examples.

I will also try and convince you that p-adic integrals are the tool of choice to tackle a number of other counting problems, seemingly less algebro-geometric, say of group-theoretic origin.

I will assume nothing more from my audience than what it takes to understand this abstract’s first sentence.