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SUMMARY:Allen Knutson (Cornell University)
DTSTART:20211130T190000Z
DTEND:20211130T200000Z
DTSTAMP:20260423T024656Z
UID:AG-Davis/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AG-Davis/42/
 ">The commuting scheme and generic pipe dreams</a>\nby Allen Knutson (Corn
 ell University) as part of UC Davis algebraic geometry seminar\n\n\nAbstra
 ct\nThe space of pairs of commuting matrices is more mysterious than you m
 ight think -- in particular\, Hochster's 1984 conjecture that it is reduce
 d remains unresolved. I'll explain how to degenerate it to one component o
 f the "lower-upper scheme" {(X\,Y) : XY lower triangular\, YX upper triang
 ular}\, a reduced complete intersection\, and how to compute the degree of
  any component as a sum over "generic pipe dreams". As a consequence\, thi
 s recovers both the "pipe dream" and "bumpless pipe dream" formulae for do
 uble Schubert polynomials. Some of this work is joint with Paul Zinn-Justi
 n.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/42/
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