Combinatorics Seminar: "Springer fibers and the Delta Conjecture"

Abstract: Springer fibers are a family of varieties that have remarkable connections to representation theory and combinatorics. In particular, Springer constructed an action of the symmetric group on the cohomology ring of a Springer fiber, and used it to geometrically construct the Specht modules (in type A), which are the irreducible representations of the symmetric group. In this talk, I will introduce a new family of varieties generalizing the Springer fibers and show how they are connected to the Delta Conjecture from algebraic combinatorics (the "rise" half of the conjecture was recently proven). We’ll then use these varieties to geometrically construct the induced Specht modules. This is joint work with Jake Levinson and Alexander Woo.

Host: Martha Precup