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Speaker: Alexander Black (Bowdoin College)

Title: Non-symmetric Macdonald Polynomials and Graph Coloring 

Abstract: Many polynomials in algebraic combinatorics are defined implicitly, so even describing their supports,  the sets of monomials that appear with nonzero coefficient, is nontrivial. One approach to this question is to show the saturated Newton polytope property, which says that a monomial is in the support if and only if its exponent vector is contained in an associated polytope called its Newton polytope. In 2019, Monical, Tockan, and Yong conjectured that this property holds for non-symmetric Macdonald polynomials, a beautiful and prominent family of polynomials from statistical mechanics and representation theory. In this talk, I will introduce a novel interpretation of non-symmetric Macdonald polynomials from a combinatorial viewpoint using graph coloring and discuss how I used this perspective to prove this conjecture in joint work with Milo Bechtloff Weising.