David Anderson: Degeneracy loci in geometry and combinatorics

(08 mars 2024/March 08, 2024) Colloque des sciences mathématiques du Québec/CSMQ. www.crmath.ca/en/activities/#...
David Anderson: Degeneracy loci in geometry and combinatorics
Abstract: Given a matrix of homogeneous polynomials, there is a “degeneracy locus” of points where specified submatrices drop rank. These loci are ubiquitous, and formulas for their degrees go back to Cayley and Salmon in the mid-1800s. The search for more general and refined degree formulas led to a rich interaction between geometry and combinatorics in the late 20th century, and that interplay continues today. I will describe recent and new formulas relating the geometry of degeneracy loci with the combinatorics of Schubert polynomials, including some ongoing joint work with William Fulton.