Department of Mathematics Fall 2026 Colloquium Series - Prof. Mark Skandera

Picturing a change-of-basis matrix

Prof. Mark Skandera, Lehigh University

Abstract: Much work in algebraic combinatorics involves the comparison of two different bases of a vector space, and pictorial formulas for entries of the change-of basis matrix that relates the two bases.

Such formulas tell us how to compute a matrix entry by drawing certain pictures and playing a game with them. In one vector space known as the Hecke algebra, a certain basis defined by Kazhdan and Luszig and another natural basis are related by a change-of basis matrix having no known elementary formula. We will look at pictures and games which describe some entries of this matrix, and at the open problem of describing the remaining entries.

This is joint work with Tommy Parisi, Ben Spahiu, and Jiayuan Wang.

The talk will be accessible to students who have taken linear algebra.

Tea and refreshments available from 3:00-3:25 p.m. in the Assmus Conference Room (CU 212).

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