math

My PhD was in mathematical physics and topology, often at the interface between the two. I worked on field theories and anomalies, knot homologies, and homotopy theory, using tools from algebraic topology and higher category theory to study structures in quantum field theory such as anomalies, symmetry breaking, and dualities.

Over the course of my PhD I wrote around ten papers with collaborators across mathematics and physics. You can find the full list on the papers page.

Talks and Posters

• GSTGC 2022 talk on Virasoro and differential cohomology.
• PI GCS 2022 poster on A Long Exact Sequence on Symmetry Breaking.
• UCLA 2022 Algebraic Topology Seminar talk on Stratification in Physical Systems (in progress).
• APS March meeting 2023 on Symmetry breaking phase and crystalline phases: CEP, anomaly matching, and LSM (in progress).
• NEAT MAPS 2023 talk on Braided monoidal 2-categories and knot homologies.
• Top order and category theory seminar 2023 talk on Abelian duality and topological field theories.
• Courcher 2023 summer school on Quantum Entanglement and Toplogy poster on Long Exact Sequence on Symmetry Breaking.
• Purdue 2023 Topology seminar on En algebras in m categories (in progress).
• CMSA Quantum Matter in Math and Physics (Nov 2023) on Long exact sequence in symmetry breaking. See here for the recording of the video.
• Amherst Topology seminar on Stratification in Physical Systems(in progress).
• 2024 San Juan Algebraic structures in topology conference on Braided monoidal 2-categories and knot homologies.

Curriculum vitae

• Curriculum vitae (June 2026)

Miscellaneous

Minor thesis

Khovanov Homology and Knot Instanton Homology.

Seminars organized

• Trivial Notion II (Spring 2023)
• Trivial Notion (Fall 2023)
• Topological Order (Fall 2022)
• Reflection Positivity and Invertible Topological Phases (Spring 2022)
• Electric Magnetic Duality (2020)

CS projects

• Aplite: A purely functional statically-typed lightweight programming language with emphasis on composibility and run-time guarantees by type-checking.
• Kubernetes Operator in Aplite: A Kubernetes "client library" for Aplite. Really a Kubernetes operator run as a pod in the cluster with a server that communicates with the local Aplite server. Currently written in Python.
• Arend documentation of HoTT: An ongoing project to code/verify all the theorems in Homotopy Type Theory: an Univalent Foundation in Arend, a formal verification system that uses homotopy type theory (it assumes the univalence axiom).