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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240523T140000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-li-yu
SUMMARY:Algebraic and Enumerative Combinatorics - Li Yu
CLASS:PUBLIC
DESCRIPTION:TITLE: Integrable systems on the dual space of Lie algebras ari
 sing\nfrom log-canonical cluster structures\n\nSPEAKER:\n Li Yu\n\nAFFILIA
 TION:\n University of Toronto\n\nLOCATION:\n MC 6029\n\nThere will be a pr
 e-seminar presenting relevant background at the\nbeginning graduate level 
 starting at 1pm.\n\nABSTRACT: Let $(X\, \\{~\,~\\})$ be an (affine) Poisso
 n variety. A\nlog-canonical cluster structure on $X$ is a cluster structur
 e on the\ncoordinate ring of $X$ such that $\\{\\phi\, \\psi\\} = \\text{c
 onst} \\cdot\n\\phi \\psi$ whenever $\\phi\, \\psi$ are cluster variables 
 which belong to\nthe same cluster. When the Poisson bivector vanishes at s
 ome point $x\n\\in X$\, the tangent space $T_x X$ comes equipped with a Po
 isson\nbracket $\\{~\,~\\}^{\\text{lin}}$\, the linearization of $\\{~\,~\
 \}$. \nGiven a function $\\phi$ on $X$\, we propose a way of linearizing 
 it to\nget a function $\\phi^{\\text{lin}}$ on $T_x X$. Very often\, when\
 n$\\{\\phi_1\, \\cdots\, \\phi_n\\}$ is a cluster in a log-canonical clust
 er\nstructure on $(X\, \\{~\,~\\})$\, $\\{\\phi_1^{\\text{lin}}\, \\cdots\
 ,\n\\phi_n^{\\text{lin}}\\}$ is an integrable system on $(T_x X\,\n\\{~\,~
 \\}^{\\text{lin}})$.  We present two scenarios where this is the\ncase.
DTSTAMP:20261010T232913Z
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