Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

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Algebra-Geometry-Combinatorics Seminar

Event Type
Seminar/Symposium
Sponsor
Department of Mathematics
Location
345 Altgeld Hall
Date
Oct 16, 2025   2:00 pm  
Speaker
Mark Skandera
Contact
Alexander Yong
E-Mail
ayong@illinois.edu
Views
3
Originating Calendar
General Events - Department of Mathematics

Speaker: Mark Skandera (Lehigh University)

Abstract: The Kazhdan-Lusztig basis {C'_w | w in S_n} of the Hecke algebra H_n is related to the natural basis {T_v | v in S_n} of H_n by a matrix whose entries are recursively-defined polynomials {P_{v,w}(q) | v,w in S_n} in N[q] known as the Kazhdan-Lusztig polynomials.  No known combinatorial formula interprets the coefficients of these polynomials as set cardinalities.  Nevertheless, some results which depend upon pattern avoidance in the permutation w permit one to factor the Kazhdan-Lusztig basis element C'_w in a way which provides combinatorial formulas for coefficients of the polynomials {P_{v,w}(q) | v in S_n} having second index w.  No characterization of the permutations w permitting such a factorization is known. We present a negative result: conditions on w which imply that such a factorization does not exist.

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