BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//132.216.98.100//NONSGML kigkonsult.se iCalcreator 2.20.4//
BEGIN:VEVENT
UID:20250709T210813EDT-0195Vc7eBg@132.216.98.100
DTSTAMP:20250710T010813Z
DESCRIPTION:CIRGET Algebraic Geometry Seminar\n\nTitle: Polynomial integrab
 le systems from cluster structures\n\nAbstract: We present a general frame
 work for constructing polynomial integrable systems with respect to linear
 izations of Poisson varieties that admit log-canonical coordinate systems.
  Our construction is in particular applicable to Poisson varieties with co
 mpatible cluster or generalized cluster structures. As special cases\, we 
 consider an arbitrary standard complex semisimple Poisson Lie group $G$ wi
 th the Berenstein-Fomin-Zelevinsky cluster structure\, nilpotent Lie subgr
 oups of $G$\, identified with Schubert cells in the flag variety of $G$\, 
 with the standard cluster structure\, and the dual Poisson Lie group of ${
 \rm GL}(n\, \mathbb C)$ with the Gekhtman-Shapiro-Vainshtein generalized c
 luster structure. In each of the three cases\, we show that every extended
  cluster in the respective cluster structure gives rise to a polynomial in
 tegrable system on the respective Lie algebra with respect to the lineariz
 ation of the Poisson structure at the identity element. In the third examp
 le\, we obtain an integrable system on $(\mathfrak{gl}(n\, \mathbb C)^*\, 
 \pi_{KKS})$ which is different from the well-known Gelfand-Zeitlin system.
  For some of the integrable systems thus obtained\, we give Lie theoretic 
 interpretations of their Hamiltonians\, and we further show that all their
  Hamiltonian flows are complete.\n\nNo prior knowledge of cluster algebras
  is required.\n\nThis is joint work with Yanpeng Li and Jiang-Hua Lu.\n\nI
 n person: Location: UQAM PK-5675\n
DTSTART:20241120T200000Z
DTEND:20241120T210000Z
SUMMARY:Yu Li (University of Toronto)	
URL:/mathstat/channels/event/yu-li-university-toronto-
 361266
END:VEVENT
END:VCALENDAR