Sponsored by the UW Department of Mathematics and the Pacific Institute for the Mathematical Sciences.
February 10, 2017 at 2:30pm SMI 102 

Patricia Hersh North Carolina State University 
Poset topology meets combinatorial representation theory 
Back in the 1960's, GianCarlo Rota recognized the importance of an interpretation for the coefficients in inclusionexclusion counting formulas as reduced Euler characteristics of associated simplicial complexes. We will begin by discussing some of the history of this powerful link between combinatorics and topology. Then we will turn to the example of weak Bruhat order. This partial order on permutations captures much of the structure of how permutations may be written as products of adjacent transpositions. The relations satisified by the adjacent transpositions, the braid relations, may be shown to control a poset invariant called the Moebius function  the aforementioned reduced Euler characteristic in disguise. A topological result of Quillen, the Quillen Fiber Lemma, enables key properties of weak Bruhat order to be transferred to posets of current interest in the representation theory of KacMoody algebras, the socalled crystal graphs of highest weight representations. However, computer computations of the Moebius function for crystal graphs led us also to discover unexpected new relations amongst the crystal raising and lowering operators. This work on crystal graphs is joint work with Cristian Lenart. 

March 13, 2017 at 2:30pm TBD 

Chelsea Walton Temple University 
TBA 


March 31, 2017 at 2:30pm TBD 

John Urschel Massachusetts Institute of Technology 
TBA 


April 7, 2017 at 2:30pm SMI 102 

Qing Han University of Notre Dame 
TBA 


April 21, 2017 at 2:30pm TBD 

Robert McCann University of Toronto 
TBA 


April 28, 2017 at 2:30pm TBD 

Maciej Zworski University of California, Berkeley 
TBA 


May 12, 2017 at 2:30pm TBD 

Candice Price University of San Diego 
TBA 


May 26, 2017 at 2:30pm TBD 

Piper Harron University of Hawaii at Manoa 
TBA 

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