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SUMMARY:Gamma class\, total positivity and mirror symmetry [MPIM]
DTSTART:20250313T140000Z
DTEND:20250313T150000Z
DTSTAMP:20260809T201100Z
UID:indico-event-271@math-events.uni-bonn.de
DESCRIPTION:Speakers: Chi Hong Chow (MPIM)\n\nMPI-Oberseminar\nMirror symm
 etry predicts that for any Fano manifold $X$ there should be a Landau-Ginz
 burg model $(X^{\\vee}\,W)$ such that the quantum $D$-module of $X$ is iso
 morphic to the Gauss-Manin system of $(X^{\\vee}\,W)$. In addition\, the n
 atural lattice structures on the spaces of flat sections of these $D$-modu
 les\, one coming from the image of the Chern character of $X$ and one from
  certain integral relative homology of $X^{\\vee}$\, should match\, after 
 the former is twisted by the Gamma class. These predictions have been veri
 fied for toric Fano manifolds.\nIn this talk\, I will discuss the case whe
 n $X$ is a flag variety of arbitrary Lie group type\, where $(X^{\\vee}\,W
 )$ is known to be the Rietsch mirror. I will focus on $1=ch([\\mathcal{O}_
 X])$ and explain the result that this element corresponds to the totally p
 ositive part of $X^{\\vee}$ in the sense of Lusztig. If time permits\, I w
 ill explain how to apply this result to prove Gamma conjecture I for these
  varieties. \n \n\nhttps://math-events.uni-bonn.de/event/271/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/271/
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