Geometrification of monodromy for hypergeometric systems

Tuesday, 9-April-2024 

Abstract

The Gauss hypergeometric equation controls solutions of second-order linear differential equations with three regular singular points. These solutions encompass a zoo of special functions, with rich and useful structure. Moving the complex variable around a singular point in the domain leads to a monodromy action on the solutions. I will explain a 'geometrification' of this action, using the K-theory of Calabi-Yau 3-folds. If time permits, I will introduce work in progress with Weilin Su extending this to multi-parameter analogs of the Gauss equation, via a further 'categorification' using the derived category of coherent sheaves.