Research Interests

Quantum field theory (QFT) is an enormously successful theoretical framework that physicists have used to understand the physics of very small particles. The theory has had made many surprising predictions that have been confirmed by experiment, and these predictions have been verified to a great degree of accuracy. The mathematical language necessary to make precise sense of QFT, however, remains incomplete: to make their predictions, physicists have proceeded via an intuitive approach that has resisted packaging into axioms, lemmas, and theorems. More precisely, though a number of beautiful axiomatizations of the notion of a QFT exist, it is quite difficult to rigorously construct examples of such in a way that resembles what the physicists do in practice.

I am broadly interested in this question, but in practice, my research has focused on an approach to (perturbative) QFT developed by Kevin Costello and Owen Gwilliam. The main elements of this approach involve renormalization, the Batalin-Vilkovisky formalism, and factorization algebras. My research using these techniques falls into three broad categories:


BV Quantization of the Free Fermion


  1. The Batalin-Vilkovisky Formalism and the Determinant Line Bundle. August 2019. Journal of Geometry and Physics. DOI: 10.1016/j.geomphys.2020.103792

  2. A Mathematical Analysis of the Axial Anomaly. November 2017. Letters in Mathematical Physics. DOI: 10.1007/s11005-018-1142-4

Factorization Algebras for Bulk-Boundary Systems

In my PhD dissertation, I have extended the results of Costello and Gwilliam for field theories on manifolds with boundary. In the approach I develop, which builds on work of Dylan Butson and Philsang Yoo, one chooses a boundary condition for the field theory. The term "bulk-boundary system" refers to a field theory together with a boundary condition. The terminology is meant to invoke the idea that the theory determined by the boundary condition "couples to" or "interacts with" the theory on the interior of the spacetime manifold.

  1. A Classical Bulk-Boundary Correspondence. February 2022.

  2. Factorization Algebras for Bulk-Boundary Systems. May 2021. PhD Dissertation. Chapters 2 and 3 of the dissertation are versions of the two preprints immediately below. Chapters 4 and 5 are currently being prepared as standalone papers as well.

  3. Factorization Algebras for Classical Bulk-Boundary Systems. August 2020.

  4. Factorization algebras and abelian CS/WZW-type correspondences. January 2020. Joint with Owen Gwilliam and Brian Williams. To appear in Pure and Applied Mathematics Quarterly.


Quantization of Topological-Holomorphic Theories

  1. Quantization of topological-holomorphic field theories: local aspects. July 2021. Joint with Owen Gwilliam and Brian Williams. Accepted to Communications in Analysis and Geometry.