The focal point of my research is mathematics related to gravitation. The primary drivers of my work are stacks, homological algebra, and related categorical tools, as well as more traditional tools of the trade, like differential geometry and geometric and functional analysis.
My most active project is to better understand black hole entropy: my collaborators and I are exploring how the Batalin-Vilkovisky (BV) formalism and the theory of factorization algebras, as introduced by Costello and Gwilliam, are useful in answering questions about black hole thermodynamics. The reliance on conservation laws and the topology and geometry of spacetime submanifolds in the study of black hole entropy is evidence that the BV/factorization algebra viewpoint will be useful in deepening our understanding of this important subject.
Projects for the longer term include studying how gravitational anomalies are related to black hole thermodynamics, developing nonperturbative examples within the BV formalism, and better understanding how entropy more broadly defined can be studied using differential geometry and category theory. This last project in particular will provide good opportunities to involve undergraduates in research or expository projects.
My full-length research statement is available upon request.
A Homological Approach to Path Integration. Monograph in preparation for publication in Progress in Mathematical Physics.
General Covariance from the Viewpoint of Stacks. March 2023 Letters in Mathematical Physics. DOI: 10.1007/s11005-023-01653-3 (also available at arXiv:2112.15473v2).
Mount Holyoke College Math/Stat Club: A Geometer's Perspective on Black Hole Thermodynamics, February 2025.
Northeastern University Geometry, Physics, and Representation Theory Seminar: Factorization Algebras for Black Hole Entropy, November 2024.
CUNY Graduate Center Topology, Geometry, and Physics Seminar: Factorization Algebras for Black Hole Entropy, October 2024.
Montana State University Math Seminar: Factorization Algebras for Black Hole Entropy, September 2024.
Rutgers University-New Brunswick Math/Physics Research Group Seminar: General Covariance with Stacks, May 2022.
Northeastern University Geometry, Physics, and Representation Theory Seminar: General Covariance with Stacks, February 2022.
Boston University Geometry and Physics Seminar: General Covariance from the Viewpoint of Stacks, December 2021.
Notre Dame Topology Seminar: General Covariance from the Viewpoint of Stacks, October 2021.
Higher Structures in QFT and String Theory, a Virtual Conference for Junior Researchers: Anomalies from General Covariance, July 2021.
University of Connecticut Math/Physics Learning Seminar: A Bird's-Eye View of Anomalies, February 2021.
From Spring 2023 through Fall 2024, I led the weekly Stacks and Physics Learning Seminar at Rutgers New Brunswick. During Spring 2025, Larry Frolov and I co-organized a learning seminar in mathematical physics covering a broader set of topics. Notes from these lectures and discussions will coalesce to form my PMP monograph "A Homological Approach to Path Integration".
Rutgers University-New Brunswick Math/Physics Research Group Seminar: The Batalin-Vilkovisky Formalism and Factorization Algebras, December 2023.
Rutgers University-New Brunswick Math/Physics Research Group Seminar: A Homological Approach to Path Integration, September 2023.
Rutgers University-New Brunswick Graduate Algebra and Representation Theory Seminar (GARTS): Toward Formal Derived Geometry, April 2023.
Rutgers University-New Brunswick Lie Group/Quantum Math Seminar: An Introduction to the Batalin-Vilkovisky Formalism (and Factorization Algebras), November 2022.
UMass Math/Physics Seminar: Introduction to General Covariance with Stacks, December 2021.
UMass GRASS: The Atiyah-Singer Index Theorem, October 2020.
UMass Graduate Student Seminar (GRASS): The Loop Space/Suspension Adjunction, March 2019.
My doctoral dissertation, General Covariance with Stacks and the Batalin-Vilkovisky Formalism, contains a less general version of arXiv:2112.15473v2, as well as commentary contextualizing my research program.
My undergraduate senior thesis, The Geometry of Spacetime and its Singular Nature, was written under the direction of Prof. Lan-Hsuan Huang: it is a short introduction to general relativity with a focus on the Hawking/Penrose singularity theorems.