Combinatorics 2010: Advances, Trends & Speculations (CATS 2010 Workshop)

University Of Kentucky Research Foundation, Lexington KY

Investigators

Abstract

Combinatorics 2010: Advances, Trends & Speculations (CATS 2010 Workshop) will be held at the University of Kentucky on March 26, 2010. Four one-hour keynote addresses will be given by Sara Billey (U Washington), Patricia Hersh North Carolina State), Isabella Novik (U Washington) and Stephanie van Willigenburg (U British Columbia). This workshop dovetails with the special session "Advances in Algebraic & Geometric Combinatorics" occurring at the American Mathematical Society meeting the following two days in Lexington, KY where sixteen of the workshop participants will be giving talks. Besides the four speakers, at least twenty-five additional researchers are expected to participate in the workshop. The CATS 2010 Workshop highlights four of the major research themes in combinatorics: Coxeter groups, topological combinatorics, polytopes and manifolds, and quasisymmetric functions in representation theory. Topics of discussion will include understanding affine Grassmannians (connections with Hilbert schemes, determining a Schur function analogue for its (co)homology), total positivity from a topological perspective (for regular cell complexes, Bruhat order), face vector questions for polytopes and manifolds (the Charney-Davis conjecture, the g-conjecture for spheres and manifolds, lower bound theorem for spheres, manifolds and pseudomanifolds), and combinatorial properties of quasisymmetric Schur and skew-quasisymmetric Schur functions. A number of the workshop participants are engaged in research spanning more than one of the four areas, so their presence will help foster the interdisciplinary goals of the workshop. The workshop schedule includes ample time for workshop participants to establish new research contacts, discuss open problems and determine possible new avenues of research. The award provides full funding for the invited speakers and partial funding for the workshop participants. The workshop includes researchers at all stages of their careers, including graduate students and recent PhDs, and has a strong representation of groups which are underrepresented in mathematics.