Andrew Neitzke | Abelianization in analysis of ODEs
CMSA Math Science Lectures in Honor of Raoul Bott: Andrew Neitzke Wednesday, Oct. 16, 2024 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.
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