UIUC Dept. of Mathematics Seminar Calendar

     August 2010           September 2010          October 2010    
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  1  2  3  4  5  6  7             1  2  3  4                   1  2
  8  9 10 11 12 13 14    5  6  7  8  9 10 11    3  4  5  6  7  8  9
 15 16 17 18 19 20 21   12 13 14 15 16 17 18   10 11 12 13 14 15 16
 22 23 24 25 26 27 28   19 20 21 22 23 24 25   17 18 19 20 21 22 23
 29 30 31               26 27 28 29 30         24 25 26 27 28 29 30
                                               31

Wednesday, September 29, 2010

Algebra, Geometry and Combinatorics Seminar
3:00 pm in 7 Illini Hall, Wednesday, September 29, 2010

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Submitted by ecsima.

Alexander Yong (UIUC Math)
Drift configurations
Abstract: I'll describe a parallel between two families of polynomials defined on pairs of permutations in the symmetric group. The first family consists of the celebrated Kazhdan-Lusztig polynomials from the representation theory of Hecke algebras. The second is comprised of the h-polynomials of local rings of Schubert varieties. This parallel is formalized with a conjectural positivity and semicontinuity property for the coefficients of the second family (respectively, analogues of theorems of D. Kazhdan-G. Lusztig, and of R. Irving). These conjectures are proved for Grassmannians, by introducing new "drift configuration" models for the polynomials. This is based on joint work with L. Li.