Thesis Defense: Complexity of the zero set of a matrix Schubert ideal

Abstract: T-varieties are normal varieties equipped with an action of an algebraic torus T. The complexity of a T-variety is the codimension of the largest T-orbit. Matrix Schubert varieties are T-varieties consisting of n-by-n matrices that satisfy certain constraints on the ranks of their submatrices. Every matrix Schubert variety can be written as the product of an affine subvariety and a k-dimensional complex space, where k is as large as possible. In this talk, we focus on the complexity of these affine subvarieties endowed with a naturally defined torus action. We address the question of determining which nonnegative integers can be achieved as the complexity of one of our varieties of interest.

Faculty Advisor: John Shareshian