Seminar Event Detail


Combinatorics

Date:  Friday, January 08, 2016
Location:  4088 East Hall (3:10 PM to 4:00 PM)

Title:  Puzzles and equivariant K-theory of Grassmannians

Abstract:   The cohomology of the Grassmannian has a basis of Schubert classes. The structure constants for this basis, the celebrated Littlewood-Richardson coefficients, are calculated by any of the Littlewood-Richardson rules. This story has been extended to K-theory by A. Buch (2002) and to torus-equivariant cohomology by A. Knutson-T. Tao (2003). It is natural to unify these theories via a combinatorial rule for structure coefficients in equivariant K-theory. In 2005, A. Knutson-R. Vakil used puzzles to conjecture such a rule. Recently we proved the first combinatorial rule for these coefficients. Using our new rule, we construct a counterexample to the Knutson-Vakil conjecture and prove a mild correction to it. (Joint work with Alexander Yong)


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Speaker:  Oliver Pechenik
Institution:  U. Illinois (Urbana-Champaign)

Event Organizer:   Sergey Fomin   

 

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