I am interested in applying tools from algebraic geometry to problems in noncommutative algebra and representation theory. My advisor is David Ben-Zvi in the Geometry Research Group.
Joint with David Jordan: we are studying the geometric structure underlying the lower central series of associative algebras. Preprint available here.
Joint with Pavel Safronov: we are studying global Cherednik algebras from the perspective of factorization spaces.
In May of 2011, I presented at the MIT Talbot Workshop.
In June of 2011, I participated in the workshop on Cluster Algebras and Lusztig's Semicanonical Basis.
In June of 2011, I attended the ICMS conference on Noncommutative Algebra and its Applications.
In the Fall of 2011, I organized a learning seminar on etale cohomology.
In June 2012, I participated in the MSRI summer school on Noncommutative Algebraic Geometry.
In August 2012, I spoke at Categorical Representation Theory at the University of Oregon.
In April 2013, I gave an outreach talk/activity for elementary through high school students as part of UT's Sunday Math Circle.
In April 2013, I participated in the MSRI workshop "Interactions between Noncommutative Algebra, Representation Theory, and Algebraic Geometry".
In June 2013, I presented at GAeL XXI in Stockholm.
In August 2013, I participated in the workshop Quantum/Affine Schubert Calculus at the University of Oregon.
In Fall 2012, I gave a talk about Koszul duality in representation theory for the UT Graduate Geometry and Topology Seminar. Notes by James Pascaleff available here.
Here are the notes for my August 2012 talk introducing the basic ideas in the theory of algebraic D-modules for Categorical Representation Theory at the University of Oregon.
Here are my lecture notes from the 2011 MIT Talbot workshop in which I discuss the construction of three moduli spaces associated to a complex projective variety (the Betti, Dolbeault, and de Rham moduli spaces).
Here are some lecture notes from my July 2011 PhD candidacy talk on the Beilinson-Bernstein localization theorem. Surely typo-ridden.
Here is a summary I wrote of Bernstein, Gel'fand, and Ponomarev's paper "Coxeter Functors and Gabriel's Theorem". Beware of typos.