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SUMMARY:Yuancheng Xie (Peking University)
DTSTART:20230203T090000Z
DTEND:20230203T103000Z
DTSTAMP:20260423T024801Z
UID:BIMSA-ISS/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BIMSA-ISS/4/
 ">On the full Kostant-Toda lattice and the flag varieties</a>\nby Yuanchen
 g Xie (Peking University) as part of BIMSA Integrable Systems Seminar\n\n\
 nAbstract\nIn 1967\, Japanese physicist Morikazu Toda proposed an integrab
 le lattice model to\ndescribe motions of a chain of particles with exponen
 tial interactions between nearest\nneighbors. Since then\, Toda lattice an
 d its generalizations have become the test models\nfor various techniques 
 and philosophies in integrable systems and wide connections are\nbuilt wit
 h many other branches of mathematics. In this talk\, I will characterize s
 ingular\nstructure of solutions of the so-called full Kostant-Toda (f-KT) 
 lattices defined on simple\nLie algebras in two different ways: through th
 e τ-functions and through the Kowalevski-\nPainlevé analysis. Fixing the
  spectral parameters which are invariant under the f-KT flows\,\nwe build 
 a one to one correspondence between solutions of the f-KT lattices and poi
 nts in\nthe corresponding flag varieties.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/4/
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