Geometry and Topology Seminar - Jenna Rajchgot - Determinants, Schubert varieties, and quiver representation varieties
Title: Determinants, Schubert varieties, and quiver representation varieties.
Abstract: Determinantal varieties are algebraic varieties defined by the simultaneous vanishing of minors of matrices. They are important in algebraic geometry because many naturally occurring algebraic varieties are determinantal.
After reviewing some of these ideas, I'll focus on two families of algebraic varieties:
(i) Schubert varieties in flag varieties and multiple flag varieties; and
(ii) representation varieties of Dynkin quivers.
The study of each family is motivated by questions in algebraic geometry and representation theory and has led to beautiful combinatorics.
Furthermore, each family contains, as special cases, classes of determinantal varieties of independent interest.
I'll discuss an ongoing research program on unifying problems about the equivariant geometry of representation varieties of Dynkin quivers with the corresponding problems for Schubert varieties in multiple flag varieties (joint with R. Kinser), as well as some consequences for degeneracy loci (joint with R. Kinser and A. Knutson).