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URL:/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-allen
SUMMARY:Algebraic and enumerative combinatorics seminar-Allen Knutson
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE: Schubert calculus by counting puzzles\n\nSp
 eaker\n Allen Knutson\n\nAffiliation\n Cornell\n\nLocation\n MC 5479\n\n 
 ABSTRACT: There are three rings-with-bases whose multiplicative\nstructur
 e constants are computed by the same rule: the cohomology ring\nof the Gra
 ssmannian Gr(k\,n)\, the representation ring of GL_k (made by\nstabilizing
  the previous in n)\, and one made by summing all\nrepresentation rings of
  the symmetric groups (made by stabiliizing the\nprevious in k). The most 
 famous rules\, typically involving counting\nYoung tableaux\, are for the 
 most stable version\, but the unstable\nversion admits the most generaliza
 tions\, to K-theory\, equivariant\ncohomology\, quantum cohomology\, and t
 o other homogeneous varieties.\nI'll explain how to compute the multiplica
 tion in many of these cases\nby counting \"puzzles\".\n\nThis work is join
 t with Terry Tao and Paul Zinn-Justin.\n\nTHERE WILL BE A PRE-SEMINAR PRES
 ENTING RELEVANT BACKGROUND AT THE\nBEGINNING GRADUATE LEVEL STARTING AT 1P
 M\,\n 
DTSTAMP:20250824T145034Z
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