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.
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.