CMSA/Math Science Lectures in Honor of Raoul Bott

Organizers：

CMSA, Harvard University

Speaker：

Andrew Neitzke

Yale University

Time：

Thur., 04:00 am, Oct. 17, 2024 (Beijing time)

Online：

Zoom Webinar Registration

https://harvard.zoom.us/webinar/register/WN_FdXunKh_TmmLF0GxpPwAYg#/registration

Title：

Abelianization in analysis of ODEs

Abstract:

I will describe the exact WKB method for asymptotic analysis of families of ODEs in one variable, and its interpretation as a kind of abelianization procedure, which replaces GL(N)-connections over a Riemann surface by GL(1)-connections over an N-fold branched cover. This abelianization procedure connects exact WKB to various subjects in geometry (cluster algebras, moduli of Higgs bundles, enumerative geometry). One application is a conjectural description of Hitchin’s hyperkahler metric on the moduli of Higgs bundles; I will review some recent progress on these conjectures.