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SUMMARY:Leonid Monin (Bristol)
DTSTART:20200618T123000Z
DTEND:20200618T133000Z
DTSTAMP:20260423T005800Z
UID:notts_ag/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/notts_ag/10/
 ">Inversion of matrices\, a $\\C^*$ action on Grassmannians and the space 
 of complete quadrics</a>\nby Leonid Monin (Bristol) as part of Online Nott
 ingham algebraic geometry seminar\n\n\nAbstract\nLet $\\Gamma$ be the clos
 ure of the set of pairs $(A\,A^{-1})$ of symmetric matrices of size $n$. I
 n other words\, $\\Gamma$ is the graph of the inversion map on the space $
 \\mathrm{Sym}_n$ of symmetric matrices of size $n$. What is the cohomology
  class of $\\Gamma$ in the product of projective spaces? Equivalently\, wh
 at is the degree of the variety $L^{-1}$ obtained as the closure of the se
 t of inverses of matrices from a generic linear subspace $L$ of $\\mathrm{
 Sym}_n$. This question is interesting in its own right but it is also moti
 vated by algebraic statistics. In my talk\, I will explain how to invert a
  matrix using a $\\C^*$ action on Grassmannians\, relate the above questio
 n to classical enumerative problems about quadrics\, and give several poss
 ible answers.\n\nThis is joint work in progress with Laurent Manivel\, Mat
 eusz Michalek\, Tim Seynnaeve\, Martin Vodicka\, Andrzej Weber\, and Jaros
 law A. Wisniewski.\n
LOCATION:https://researchseminars.org/talk/notts_ag/10/
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