Speaker: Prof. Ted Chinburg

Abstract:

Capacity theory originated from studying the equilibrium distribution of charges on a plate in the plane. In this talk I will describe the surprising discovery that this theory pertains to the possible locations of conjugates of algebraic integers which are constrained to lie in a given region. It turns out that such conjugates behave in many respects like repelling electric charges. This has applications to constructing polynomials with useful boundedness and integrality properties. I will describe how such polynomials enter into cryptography. By the end of the talk I hope to describe a new frontier in the subject concerning multivariable auxiliary polynomials and higher dimensional capacity theory.