Speaker: Alex Yong, University of Illinois at Urbana-Champaign
Title: Newton polytopes in algebraic combinatorics
Abstract: A polynomial has saturated Newton polytope (SNP) if every lattice point of the convex hull of its exponent vectors corresponds to a monomial. We compile instances of SNP in algebraic combinatorics (some with proofs, others conjecturally): skew Schur polynomials; symmetric polynomials associated to reduced words, Redfield--Polya theory, Witt vectors, and totally nonnegative matrices; resultants; discriminants (up to quartics); Macdonald polynomials; key polynomials; Demazure atoms; Schubert polynomials; and Grothendieck polynomials, among others. This is joint work (arXiv:1703.02583) with Cara Monical and Neriman Tokcan.