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CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, May 13, 2021 - 3:30pm

Yusra Naqvi

University College London


University of Pennsylvania

usual zoom link

Interpolation polynomials (also known as interpolation Jack polynomials, shifted Jack polynomials, or Knop-Sahi polynomials) are a family of inhomogeneous symmetric polynomials characterized by simple vanishing properties whose top degree homogeneous components are Jack polynomials. In 1996, Knop and Sahi conjectured that, after a suitable normalisation, these polynomials have positive integral coefficients. In this talk I will describe our recent proof of this conjecture, in which we introduce a new combinatorial object called a bar game and then expand interpolation polynomials as a weighted sum of these games.

This is joint work with S. Sahi and E. Sergel.