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SUMMARY:Normal forms\, integrable systems\, and quantum periods
DTSTART:20231124T153000Z
DTEND:20231124T170000Z
DTSTAMP:20260524T053200Z
UID:indico-event-11019@indico.math.cnrs.fr
CONTACT:volodya@univ-angers.fr\;0663168700
DESCRIPTION:Speakers: Alexander Soibelman (IHES)\n\nA theorem of Sjöstran
 d says that\, under certain conditions\, one can compute the asymptotic e
 xpansions of the eigenvalues of a Schrödinger operator with polynomial po
 tential using the quantum analogue of the Birkhoff normal form. In my talk
 \, I will give a brief introduction to both the classical and quantum Birk
 hoff normal forms\, then explain how each may be interpreted geometrically
 \, in terms of an equivalence on the germs of a complex integrable system 
 or (for the quantum version) its quantization. In the latter case\, this g
 ives rise to "quantum periods"\, which may be understood either as formal 
 deformations of variations of Hodge structures or as functionals on Hochsc
 hild homology. This is joint work in progress with Maxim Kontsevich.\n\nht
 tps://indico.math.cnrs.fr/event/11019/
LOCATION:salle Maryam Mirzakhani (ex salle 201) (IHP\, Paris 75005)
URL:https://indico.math.cnrs.fr/event/11019/
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