From Total Positivity to Pure Free Resolutions, Keller VandeBogert (Notre Dame) -- April 17th, 2025

Schur functors are fundamental objects sitting at the intersection of representation theory, combinatorics, and algebraic geometry. There are many ways to try to generalize such objects, but one perspective is to view the classical Jacobi--Trudi identity as saying that Schur functors are built "with respect to" the symmetric algebra. This leads to the following question: given an arbitrary algebra A, do there exist Schur functors "with respect to" the algebra A? In this talk, I'll make this question more precise, and discuss an answer to this question which has deep connections to both the equivariant analogues of positivity in combinatorics and Boij--Soederberg theory of non-regular rings in commutative algebra. This is based on joint work with Steven V Sam.

The seminar co-organizers are Ian Cavey, Andrew Hardt, David Keating, and Alexander Yong.