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SUMMARY:Cluster integrable systems and the tame symbol
DTSTART:20230323T151500Z
DTEND:20230323T171500Z
DTSTAMP:20230610T145900Z
UID:indico-event-276@indico.hiskp.uni-bonn.de
DESCRIPTION:Speakers: Vladimir Fock (UniversitĂ© de Strasbourg et CNRS)\n\
nCluster integrable systems discovered by Goncharov and Kenyon is an appro
ach to a large class of integrable systems starting with the Poncelet pori
sm discovered 200 years ago to modern spinning tops\, Toda lattices and in
its quantum versions\, which are not yet very well understood\, lattice m
odels\, Hofstadter's butterfly and many others.\n\nThe cluster approach to
those systems interprets their phase spaces either as the space of config
urations of flags in an infinite dimensional space or as the space of pair
s (spectral curve\, line bundle on it). This dual approach allows to study
the systems in detail and of course to find their classical solutions.\n\
nHowever\, the quantization of these systems does not go as smoothly as it
s classical part. We will suggest a quasi-classical approach to those syst
ems using a tool borrowed from number theory namely the tame symbol. In it
s simplest incarnation\, tame symbol is a multiplicative analogue of the r
esidue. We use it to formulate the Bohr-Sommerfeld condition on the Lagran
gian subvarieties for the integrable systems\, thus giving the quasi-class
ical spectrum with the wave function expressed in terms of the dilogarithm
.\n\nIf time permits we will speak about some elementary applications of t
he tame symbol.\n\nNote the unusual location:\n\nKleiner HĂ¶rsaal Mathemat
ik\, 1st floor\, Wegelerstr. 10\, 53115 Bonn.\n\nhttps://indico.hiskp.uni-
bonn.de/event/276/
LOCATION:PI
URL:https://indico.hiskp.uni-bonn.de/event/276/
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