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BEGIN:VEVENT
SUMMARY:Pavlo Pylyavskyy (University of Minnesota)
DTSTART:20221102T130000Z
DTEND:20221102T143000Z
DTSTAMP:20260404T111009Z
UID:algsjtu/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/algsj
 tu/1/">Crystal Invariant Theory</a>\nby Pavlo Pylyavskyy (University of Mi
 nnesota) as part of SJTU algebra seminar\n\n\nAbstract\nAbstract: Berenste
 in and Kazhdan have introduced a birational lifting of\nKashiwara's crysta
 ls\, called geometric crystals. Their theory gives rise to\nfour families 
 of operators acting on the space of complex $m \\times n$\nmatrices\, two 
 acting by geometric crystal operators and two acting by\ngeometric R-matri
 ces. These actions can be viewed as "crystal analogues" of\nthe usual acti
 ons of $GL_m$ and $GL_n$ - and their subgroups $S_m$ and\n$S_n$ - on the p
 olynomial ring in $m \\times n$ variables. Many important\nfunctions in th
 e theory of geometric crystals are invariants of one or more\nof those act
 ions. The examples include $\\epsilon$ and $\\phi$ functions\,\nenergy fun
 ction\, decoration function\, insertion and recording tableaux of\nNoumi-Y
 amada geometric RSK\, central charge\, etc. We study generators of the\nin
 variants of one or more of the families of operators\, and obtain new\nfor
 mulas for the important functions by writing them in terms of those\ngener
 ators. The talk is based on joint work with Ben Brubaker\, Gabe\nFrieden\,
  Travis Scrimshaw\, and Thomas Lam.\n\nZoom meeting ID: 927 9300 3904\nPas
 sword: 909921\n
LOCATION:https://stable.researchseminars.org/talk/algsjtu/1/
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BEGIN:VEVENT
SUMMARY:Hoel Queffelec (Institut Montpelliérain Alexander Grothendieck)
DTSTART:20221122T020000Z
DTEND:20221122T033000Z
DTSTAMP:20260404T111009Z
UID:algsjtu/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/algsj
 tu/3/">Surface skein algebras\, categorification and positivity</a>\nby Ho
 el Queffelec (Institut Montpelliérain Alexander Grothendieck) as part of 
 SJTU algebra seminar\n\n\nAbstract\nSkein algebra for surfaces appear in q
 uantum topology as natural generalizations of the Jones polynomial to thic
 kened surfaces. They enjoy deep connections with the theory of cluster alg
 ebras\, which partly motivated the conjecture by Fock-Goncharov-Thurston t
 hat these algebras should admit a basis with positive structure constants.
 \nI will explain a proof of a version of such a conjecture based on the us
 e of categorification tools from quantum algebra.\n\nThis is based on join
 t work with Kevin Walker and Paul Wedrich\n\n\nzoom id: 936 7477 0787\npas
 word: 556794\nLink: https://ucr.zoom.us/j/93674770787?pwd=ODJLb0VvbWRwc2ZG
 UWRMMjhwZ3FqUT09\n
LOCATION:https://stable.researchseminars.org/talk/algsjtu/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xuhua He (Chinese University of Hong Kong)
DTSTART:20221109T130000Z
DTEND:20221109T143000Z
DTSTAMP:20260404T111009Z
UID:algsjtu/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/algsj
 tu/4/">Total positivity on the twisted product of flag varieties</a>\nby X
 uhua He (Chinese University of Hong Kong) as part of SJTU algebra seminar\
 n\n\nAbstract\nIn this talk\, we consider the twisted product of flag vari
 eties\, which include as special cases the double flag varieties\, the Bot
 t-Samelson varieties\, and the Braid varieties. We will explain how to use
  the (single) flag variety of Kac-Moody groups to study the twisted produc
 t of flag varieties of reductive groups. As consequence\, we will establis
 h the cellular decomposition and regularity theorem of totally positive st
 ructure on the twisted product of flag varieties. In particular\, we answe
 r an open problem of Fomin and Zelevinsky on the double Bruhat cells. This
  talk is based on a joint work with Huanchen Bao (NUS).\n\nzoom id: 971 82
 58 1676\npassword: 498175\nLink: https://ucr.zoom.us/j/97182581676?pwd=enJ
 ybUJWWFN5YWVwSTVZanZJTkVJUT09\n
LOCATION:https://stable.researchseminars.org/talk/algsjtu/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Allegretti (Tsinghua University)
DTSTART:20221116T130000Z
DTEND:20221116T143000Z
DTSTAMP:20260404T111009Z
UID:algsjtu/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/algsj
 tu/5/">Cluster algebraic structures in Teichmüller theory</a>\nby Dylan A
 llegretti (Tsinghua University) as part of SJTU algebra seminar\n\n\nAbstr
 act\nThis talk will be an introduction to the use of cluster coordinates i
 n Teichmüller theory. To motivate this topic\, I will first review a clas
 sical result\, proved independently by Nigel Hitchin and Michael Wolf\, wh
 ich provides a parametrization of the Teichmüller space of a compact surf
 ace by holomorphic quadratic differentials. I will then explain how\, if w
 e replace holomorphic differentials in this theorem by meromorphic differe
 ntials\, the corresponding Teichmüller space acquires a natural cluster s
 tructure.\n\nzoom id: 975 0835 1557\npassword：619128\nlink: https://ucr.
 zoom.us/j/97508351557?pwd=eTh1ZXlQM2dMd3gyak1xVFFiSGc2Zz09\n
LOCATION:https://stable.researchseminars.org/talk/algsjtu/5/
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