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SUMMARY:Sylvain Lacroix: Affine Gaudin models and geometric Langlands corr
 espondence
DTSTART:20260113T093000Z
DTEND:20260113T103000Z
DTSTAMP:20260425T085500Z
UID:indico-event-15480@indico.math.cnrs.fr
DESCRIPTION:Gaudin models were historically introduced as integrable spin 
 systems\, based on the Lie algebra su(2) or more generally any finite-dime
 nsional simple Lie algebra. This talk is devoted to the so-called affine G
 audin models\, which are variants associated with infinite-dimensional aff
 ine Lie algebras instead of finite ones. As such\, they possess an infinit
 e number of degrees of freedom and more precisely take the form of quantum
  field theories. They are conjecturally integrable\, in the sense of admit
 ing an infinite number of commuting conserved operators. In this talk\, I 
 will review preliminary results and conjectures on the construction of the
 se operators as well as their diagonalisation\, guided in particular by a 
 conjectural affinisation of the Geometric Langlands correspondence. This i
 s based on collaborations with G. Koutousov\, A. Molines\, J. Teschner\, B
 . Vicedo and C.A.S. Young..\n\nhttps://indico.math.cnrs.fr/event/15480/
URL:https://indico.math.cnrs.fr/event/15480/
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