Theses

My PhD thesis is titled Littlewood-Richardson Coefficents and Restriction Functors for Matroidal Schur Algebras and will be published by ProQuest.

Abstract:

The matroidal Schur algebra R(M) introduced by Braden and Mautner is an analogue of the classical Schur algebra. We show that like the classical Schur algebra, the matroidal Schur algebra has restriction functors, and the restriction multiplicities of simple modules under these functors have a combinatorial formula. We enumerate these restriction multiplicities using no-broken-circuit-bases. 

Master's Thesis:

Abstract: 

The polynomial method is an umbrella term for using polynomials to bound the possible behavior of finite collections of geometric objects such as points, lines, and other hyperplanes with respect to some geometric relation. To understand the polynomial method over finite fields we will give a brief background to, and prove, the Finite Field Kakeya Theorem, The Capset theorem, Rudnev’s bound on point-plane incidences, and Vinh’s bound on point-line incidences.