Hilbert's 13th problem and geometry

Abstract: Hilbert's 13th Problem (H13) is a fundamental open problem about polynomials in one variable. It is part of a beautiful (but mostly forgotten) story going back 3000 years. In this talk I will explain how H13 (and related problems) fits into a wider framework that includes problems in enumerative algebraic geometry and the theory of modular functions. I will then report on some recent progress, joint with Mark Kisin and Jesse Wolfson.

Mathematics

Audience: researchers in the topic

Series on open questions in Arithmetic, Geometry and Topology

Series comments: This seminar is part of the MSRI program on Random and Arithmetic Structures in Topology. The talks in this series are largely expository and focus on open questions. Registration is required. If you have any questions, please don't hesitate to contact the organizers.

Registration information for this week's seminars can be found here: Alan Reid: www.msri.org/seminars/25486 Benson Farb: www.msri.org/seminars/25556