Math Science Lectures in Honor of Raoul Bott Presented by Andrew Neitzke, Yale University Harvard University Science Center Hall D & via Zoom webinar October 16 & 17, 2024 4:00 – 5:00 pm

Wednesday, Oct. 16, 2024 4:00-5:00 pm ET

Title: Abelianization in analysis of ODEs

Abstract: I will describe the exact WKB methodfor asymptotic analysis of families of ODEs in one variable, and itsinterpretation as a kind of abelianization procedure, which replacesGL(N)-connections over a Riemann surface by GL(1)-connections over an N-fold branchedcover. This abelianization procedure connects exact WKB to various subjects ingeometry (cluster algebras, moduli of Higgs bundles, enumerative geometry). Oneapplication is a conjectural description of Hitchin’s hyperkahler metric on themoduli of Higgs bundles; I will review some recent progress on theseconjectures. 

Thursday, Oct. 17, 2024 4:00-5:00 pm ET

Title: Abelianization in quantum topology

Abstract: I will describe new applications ofabelianization to various related subjects: perturbative Chern-Simonsinvariants, skein algebras, and conformal blocks. The aim is to explain howabelianization gives a unifying perspective on constructions familiar in eachof these subjects (e.g. dilogarithmic formulas for Chern-Simons invariants,vertex models for computing quantum invariants of links, and iterated-fusionconstructions of conformal blocks for the Virasoro algebra), and also suggestsvarious extensions, which are just beginning to be explored.

Register online to attend in-person or via Zoom Webinar at: https://cmsa.fas.harvard.edu/event/mathscibott_1024/