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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Cluster algebras and discrete integrable systems -
Hone\, A (University of Kent)
DTSTART;TZID=Europe/London:20130709T140000
DTEND;TZID=Europe/London:20130709T143000
UID:TALK46147AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/46147
DESCRIPTION:We consider a large family of nonlinear rational r
ecurrence relations which arise from mutations in
cluster algebras defined by quivers. The advantage
of the cluster algebra formalism is that it immed
iately provides an invariant symplectic (or presym
plectic) structure. The problem of determining whi
ch of the recurrences are integrable in the sense
of Liouville's theorem is related to the notion of
algebraic entropy\, and via a series of conjectur
es related to tropical (max-plus) algebra\, this l
eads to a very sharp criterion for the allowed deg
rees of the terms in the recurrence. As a result\,
four infinite families of discrete integrable sys
tems are obtained. This is joint work with Allan F
ordy.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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