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SUMMARY:Linda Chen (Swarthmore College)
DTSTART:20231201T200000Z
DTEND:20231201T210000Z
DTSTAMP:20260422T212902Z
UID:MAAGC2023/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAAGC2023/1/
 ">Quantum cohomology and mirror symmetry of flag varieties</a>\nby Linda C
 hen (Swarthmore College) as part of MAAGC 2023\n\nLecture held in Temple 1
 160 VCU Monroe Park Campus.\n\nAbstract\nThe quantum cohomology ring is a 
 deformation of the ordinary cohomology ring that encodes enumerative geome
 try of curves. I will describe a natural map from a symmetric polynomial r
 ing\, which has a basis of Schur polynomials indexed by partitions\, to th
 e quantum cohomology ring of the partial flag variety\, which has a basis 
 of Schubert classes indexed by permutations or tuples of permutations.  We
  will discuss surprising properties of this map and how this proves a mirr
 or theorem for type A flag varieties. This is joint work with Elana Kalash
 nikov.\n
LOCATION:https://researchseminars.org/talk/MAAGC2023/1/
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BEGIN:VEVENT
SUMMARY:Aaron Pixton (University of Michigan)
DTSTART:20231201T220000Z
DTEND:20231201T230000Z
DTSTAMP:20260422T212902Z
UID:MAAGC2023/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAAGC2023/2/
 ">Tautological rings and competing conjectures</a>\nby Aaron Pixton (Unive
 rsity of Michigan) as part of MAAGC 2023\n\nLecture held in Temple 1160 VC
 U Monroe Park Campus.\n\nAbstract\nLet M_g be the moduli space of smooth c
 urves of genus g.  The tautological ring is a subring of the cohomology of
  M_g that was introduced by Mumford in the 1980s in analogy with the cohom
 ology of Grassmannians. It is a graded ring with one generator in each deg
 ree\, but the ideal of relations between these generators is unknown in ge
 neral. Work of Faber and Faber-Zagier in the 1990s led to two conjectures\
 , each proposing a full description of the structure of the tautological r
 ing. Both conjectures are true for g < 24\, but they contradict each other
  for g >= 24. Although these competing conjectures are both still open\, I
  will discuss some recent evidence favoring one of them over the other.\n
LOCATION:https://researchseminars.org/talk/MAAGC2023/2/
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BEGIN:VEVENT
SUMMARY:Jonah Blasiak (Drexel University)
DTSTART:20231202T140000Z
DTEND:20231202T150000Z
DTSTAMP:20260422T212902Z
UID:MAAGC2023/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAAGC2023/3/
 ">Catalania</a>\nby Jonah Blasiak (Drexel University) as part of MAAGC 202
 3\n\nLecture held in Temple 1160 VCU Monroe Park Campus.\n\nAbstract\nMany
  well-known formulas in symmetric function theory such as\nthose for Hall-
 Littlewood polynomials and the Weyl character formula\ninvolve a product o
 ver all positive roots. Replacing this product with one over an upper orde
 r ideal of positive roots (of which there are Catalan many) yields new fam
 ilies of polynomials.\nWe will see how this idea leads to elegant formulas
  for $k$-Schur functions\, their  $K$-theoretic versions\, $\\nabla s_\\la
 mbda$\, and Macdonald polynomials\, and explore how such formulas can pave
  the way to positive combinatorics.\n
LOCATION:https://researchseminars.org/talk/MAAGC2023/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Colmenarejo (North Carolina State University)
DTSTART:20231202T160000Z
DTEND:20231202T170000Z
DTSTAMP:20260422T212902Z
UID:MAAGC2023/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAAGC2023/4/
 ">The quantum Schubert world: polynomials\, posets\, and operators</a>\nby
  Laura Colmenarejo (North Carolina State University) as part of MAAGC 2023
 \n\nLecture held in Temple 1160 VCU Monroe Park Campus.\n\nAbstract\nIn th
 is talk\, we will start by discussing the Murnaghan-Nakayama rule for quan
 tum Schubert polynomials as the motivation for our research question. Then
 \, we will talk about the quantum k-Bruhat order\, the relations among the
  operators associated with it\, and what makes it so complicated to unders
 tand. This is joint work from two projects\, the first one with C. Benedet
 ti\, N. Bergeron\, F. Saliola\, and F. Sottile\, and the second one with N
 . Mayers.\n
LOCATION:https://researchseminars.org/talk/MAAGC2023/4/
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