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SUMMARY:The Exact WKB Method as Abelianisation of Connections
DTSTART;VALUE=DATE-TIME:20200124T130000Z
DTEND;VALUE=DATE-TIME:20200124T140000Z
DTSTAMP;VALUE=DATE-TIME:20200224T085740Z
UID:indico-event-5372@indico.math.cnrs.fr
DESCRIPTION:\n\nI will propose a geometric formalism for the WKB method in
terms of searching for an invariant splitting of a given oper (i.e.\, a m
eromorphic connection on a filtered vector bundle). I will explain why thi
s seems to be the correct formalism by considering the special case of an
oper which arises from a Schrödinger equation. An advantage of this poi
nt of view on the WKB method is being able to relate this operation to a m
uch more general operation on meromorphic connections\, called abelianisat
ion. Abelianisation has a nontrivial history\, but it came into spotlight
in the last decade in the context of supersymmetric gauge theories through
the work of Gaiotto-Moore-Neitzke on spectral networks. Recently\, I have
begun developing the mathematical theory of abelianisation and spectral n
etworks. I will explain how abelianisation provides a vast generalisation
of the exact WKB method. This talk is based on [arXiv:1902.03384]\, [arXiv
:1909.04011]\, and a few more papers in preparation\, including one joint
with M. Gualtieri\, K. Iwaki\, A. Neitzke.\n\n\n\n \n\nhttps://indico.mat
h.cnrs.fr/event/5372/
LOCATION:Institut Camille Jordan Fokko du Cloux
URL:https://indico.math.cnrs.fr/event/5372/
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