Informal Friday Seminar: Roffelsen -- A multi-valued perspective on Hilbert’s 21st problem

Title: A multi-valued perspective on Hilbert’s 21st problem.  

Abstract: Hilbert, in his famous address to the ICM at the turn of the twentieth
century, posed a problem on Fuchsian ODEs and monodromy now known as Hilbert’s 21st
problem.  The history of this problem, especially in the original one variable case, is
complicated.  Rather than going down this rabbit hole, I will describe some of the
beautiful mathematics that inspired and has spun out of this problem.  Topics that we
will touch on include character varieties, circular polygons, Del Pezzo surfaces,
isomonodromic deformations, Painlevé equations, singular integral equations and special
functions.  

The first seminar will be focused on the regular singular setting.  In the second, we
may turn to the irregular singular or q-difference setting.  

— Pieter Roffelsen