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SUMMARY:Linda Chen (Swarthmore College)
DTSTART:20231201T200000Z
DTEND:20231201T210000Z
DTSTAMP:20260404T094700Z
UID:MAAGC2023/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/MAAGC
 2023/1/">Quantum cohomology and mirror symmetry of flag varieties</a>\nby 
 Linda Chen (Swarthmore College) as part of MAAGC 2023\n\nLecture held in T
 emple 1160 VCU Monroe Park Campus.\n\nAbstract\nThe quantum cohomology rin
 g is a deformation of the ordinary cohomology ring that encodes enumerativ
 e geometry of curves. I will describe a natural map from a symmetric polyn
 omial ring\, which has a basis of Schur polynomials indexed by partitions\
 , to the quantum cohomology ring of the partial flag variety\, which has a
  basis of Schubert classes indexed by permutations or tuples of permutatio
 ns.  We will discuss surprising properties of this map and how this proves
  a mirror theorem for type A flag varieties. This is joint work with Elana
  Kalashnikov.\n
LOCATION:https://stable.researchseminars.org/talk/MAAGC2023/1/
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BEGIN:VEVENT
SUMMARY:Aaron Pixton (University of Michigan)
DTSTART:20231201T220000Z
DTEND:20231201T230000Z
DTSTAMP:20260404T094700Z
UID:MAAGC2023/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/MAAGC
 2023/2/">Tautological rings and competing conjectures</a>\nby Aaron Pixton
  (University of Michigan) as part of MAAGC 2023\n\nLecture held in Temple 
 1160 VCU Monroe Park Campus.\n\nAbstract\nLet M_g be the moduli space of s
 mooth curves of genus g.  The tautological ring is a subring of the cohomo
 logy of M_g that was introduced by Mumford in the 1980s in analogy with th
 e cohomology of Grassmannians. It is a graded ring with one generator in e
 ach degree\, but the ideal of relations between these generators is unknow
 n in general. Work of Faber and Faber-Zagier in the 1990s led to two conje
 ctures\, each proposing a full description of the structure of the tautolo
 gical ring. Both conjectures are true for g < 24\, but they contradict eac
 h other for g >= 24. Although these competing conjectures are both still o
 pen\, I will discuss some recent evidence favoring one of them over the ot
 her.\n
LOCATION:https://stable.researchseminars.org/talk/MAAGC2023/2/
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BEGIN:VEVENT
SUMMARY:Jonah Blasiak (Drexel University)
DTSTART:20231202T140000Z
DTEND:20231202T150000Z
DTSTAMP:20260404T094700Z
UID:MAAGC2023/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/MAAGC
 2023/3/">Catalania</a>\nby Jonah Blasiak (Drexel University) as part of MA
 AGC 2023\n\nLecture held in Temple 1160 VCU Monroe Park Campus.\n\nAbstrac
 t\nMany well-known formulas in symmetric function theory such as\nthose fo
 r Hall-Littlewood polynomials and the Weyl character formula\ninvolve a pr
 oduct over all positive roots. Replacing this product with one over an upp
 er order ideal of positive roots (of which there are Catalan many) yields 
 new families of polynomials.\nWe will see how this idea leads to elegant f
 ormulas for $k$-Schur functions\, their  $K$-theoretic versions\, $\\nabla
  s_\\lambda$\, and Macdonald polynomials\, and explore how such formulas c
 an pave the way to positive combinatorics.\n
LOCATION:https://stable.researchseminars.org/talk/MAAGC2023/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Colmenarejo (North Carolina State University)
DTSTART:20231202T160000Z
DTEND:20231202T170000Z
DTSTAMP:20260404T094700Z
UID:MAAGC2023/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/MAAGC
 2023/4/">The quantum Schubert world: polynomials\, posets\, and operators<
 /a>\nby Laura Colmenarejo (North Carolina State University) as part of MAA
 GC 2023\n\nLecture held in Temple 1160 VCU Monroe Park Campus.\n\nAbstract
 \nIn this talk\, we will start by discussing the Murnaghan-Nakayama rule f
 or quantum Schubert polynomials as the motivation for our research questio
 n. Then\, we will talk about the quantum k-Bruhat order\, the relations am
 ong the operators associated with it\, and what makes it so complicated to
  understand. This is joint work from two projects\, the first one with C. 
 Benedetti\, N. Bergeron\, F. Saliola\, and F. Sottile\, and the second one
  with N. Mayers.\n
LOCATION:https://stable.researchseminars.org/talk/MAAGC2023/4/
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