UW-PIMS Mathematics Colloquium

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, Gian-Carlo Rota recognized the importance of an interpretation for the coefficients in inclusion-exclusion 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 Kac-Moody algebras, the so-called 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

 


Colloquium Video Archive


Archives from Previous Years
    Archive of 2016-2017 colloquia
Archive of 2015-2016 colloquia   Archive of 2014-2015 colloquia
Archive of 2013-2014 colloquia   Archive of 2012-2013 colloquia
Archive of 2011-2012 colloquia   Archive of 2010-2011 colloquia
Archive of 2009-2010 colloquia   Archive of 2008-2009 colloquia
Archive of 2007-2008 colloquia   Archive of 2006-2007 colloquia
Archive of 2005-2006 colloquia   Archive of 2004-2005 colloquia
Archive of 2003-2004 colloquia   Archive of 2002-2003 colloquia
Archive of 2001-2002 colloquia   Archive of 2000-2001 colloquia
Archive of 1999-2000 colloquia   Archive of 1998-1999 colloquia



The University of Washington is committed to providing access, equal opportunity and reasonable accommodation in its services, programs, activities, education and employment for individuals with disabilities. To request disability accommodation contact the Disability Services Office at least ten days in advance at: 206.543.6450/V, 206.543.6452/TTY, 206.685.7264 (FAX), or e-mail at dso@u.washington.edu.


 

U of W Website Terms & Conditions    |    PRINTER FRIENDLY FORMAT   |   U of W Online Privacy Statement
Please send comments, corrections, and suggestions to: webmaster[at]math.washington.edu
Last modified: February 23, 2017, 09:18

Bookmark and Share