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SUMMARY:Pavlo Pylyavskyy (University of Minnesota)
DTSTART:20221102T130000Z
DTEND:20221102T143000Z
DTSTAMP:20260422T225657Z
UID:algsjtu/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/algsjtu/1/">
 Crystal Invariant Theory</a>\nby Pavlo Pylyavskyy (University of Minnesota
 ) as part of SJTU algebra seminar\n\n\nAbstract\nAbstract: Berenstein and 
 Kazhdan have introduced a birational lifting of\nKashiwara's crystals\, ca
 lled geometric crystals. Their theory gives rise to\nfour families of oper
 ators acting on the space of complex $m \\times n$\nmatrices\, two acting 
 by geometric crystal operators and two acting by\ngeometric R-matrices. Th
 ese actions can be viewed as "crystal analogues" of\nthe usual actions of 
 $GL_m$ and $GL_n$ - and their subgroups $S_m$ and\n$S_n$ - on the polynomi
 al ring in $m \\times n$ variables. Many important\nfunctions in the theor
 y of geometric crystals are invariants of one or more\nof those actions. T
 he examples include $\\epsilon$ and $\\phi$ functions\,\nenergy function\,
  decoration function\, insertion and recording tableaux of\nNoumi-Yamada g
 eometric RSK\, central charge\, etc. We study generators of the\ninvariant
 s of one or more of the families of operators\, and obtain new\nformulas f
 or the important functions by writing them in terms of those\ngenerators. 
 The talk is based on joint work with Ben Brubaker\, Gabe\nFrieden\, Travis
  Scrimshaw\, and Thomas Lam.\n\nZoom meeting ID: 927 9300 3904\nPassword: 
 909921\n
LOCATION:https://researchseminars.org/talk/algsjtu/1/
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BEGIN:VEVENT
SUMMARY:Hoel Queffelec (Institut Montpelliérain Alexander Grothendieck)
DTSTART:20221122T020000Z
DTEND:20221122T033000Z
DTSTAMP:20260422T225657Z
UID:algsjtu/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/algsjtu/3/">
 Surface skein algebras\, categorification and positivity</a>\nby Hoel Quef
 felec (Institut Montpelliérain Alexander Grothendieck) as part of SJTU al
 gebra seminar\n\n\nAbstract\nSkein algebra for surfaces appear in quantum 
 topology as natural generalizations of the Jones polynomial to thickened s
 urfaces. They enjoy deep connections with the theory of cluster algebras\,
  which partly motivated the conjecture by Fock-Goncharov-Thurston that the
 se algebras should admit a basis with positive structure constants.\nI wil
 l explain a proof of a version of such a conjecture based on the use of ca
 tegorification tools from quantum algebra.\n\nThis is based on joint work 
 with Kevin Walker and Paul Wedrich\n\n\nzoom id: 936 7477 0787\npasword: 5
 56794\nLink: https://ucr.zoom.us/j/93674770787?pwd=ODJLb0VvbWRwc2ZGUWRMMjh
 wZ3FqUT09\n
LOCATION:https://researchseminars.org/talk/algsjtu/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xuhua He (Chinese University of Hong Kong)
DTSTART:20221109T130000Z
DTEND:20221109T143000Z
DTSTAMP:20260422T225657Z
UID:algsjtu/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/algsjtu/4/">
 Total positivity on the twisted product of flag varieties</a>\nby Xuhua He
  (Chinese University of Hong Kong) as part of SJTU algebra seminar\n\n\nAb
 stract\nIn this talk\, we consider the twisted product of flag varieties\,
  which include as special cases the double flag varieties\, the Bott-Samel
 son varieties\, and the Braid varieties. We will explain how to use the (s
 ingle) flag variety of Kac-Moody groups to study the twisted product of fl
 ag varieties of reductive groups. As consequence\, we will establish the c
 ellular decomposition and regularity theorem of totally positive structure
  on the twisted product of flag varieties. In particular\, we answer an op
 en problem of Fomin and Zelevinsky on the double Bruhat cells. This talk i
 s based on a joint work with Huanchen Bao (NUS).\n\nzoom id: 971 8258 1676
 \npassword: 498175\nLink: https://ucr.zoom.us/j/97182581676?pwd=enJybUJWWF
 N5YWVwSTVZanZJTkVJUT09\n
LOCATION:https://researchseminars.org/talk/algsjtu/4/
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BEGIN:VEVENT
SUMMARY:Dylan Allegretti (Tsinghua University)
DTSTART:20221116T130000Z
DTEND:20221116T143000Z
DTSTAMP:20260422T225657Z
UID:algsjtu/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/algsjtu/5/">
 Cluster algebraic structures in Teichmüller theory</a>\nby Dylan Allegret
 ti (Tsinghua University) as part of SJTU algebra seminar\n\n\nAbstract\nTh
 is talk will be an introduction to the use of cluster coordinates in Teich
 müller theory. To motivate this topic\, I will first review a classical r
 esult\, proved independently by Nigel Hitchin and Michael Wolf\, which pro
 vides a parametrization of the Teichmüller space of a compact surface by 
 holomorphic quadratic differentials. I will then explain how\, if we repla
 ce holomorphic differentials in this theorem by meromorphic differentials\
 , the corresponding Teichmüller space acquires a natural cluster structur
 e.\n\nzoom id: 975 0835 1557\npassword：619128\nlink: https://ucr.zoom.us
 /j/97508351557?pwd=eTh1ZXlQM2dMd3gyak1xVFFiSGc2Zz09\n
LOCATION:https://researchseminars.org/talk/algsjtu/5/
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