Yu Leon Liu

Hi! I am a fourth year Harvard math graduate student. My advisor is Mike Hopkins. Before grad school, I did my undergraduate at UT Austin with Dan Freed.

I work in both math and physics, mostly in between. My primary research interest is mathematical physics, mostly field theories and anomalies. Mathematically, I am also interested in knot homologies and homotopy theory. Besides math and physics, I am also interested in CS (DevOps, kubernetes, type theory and functional programming languages).

Right now I am trying to start up a new blog!

Notes

Minor thesis on Khovanov Homology and Knot Instanton Homology.

Slides 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.

Quick Links

• Curriculum vitae

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 Opeator 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: This is an ongoing project to code/verify all the theorems in Homotopy Type Theory: an Univalent Foundation in Arend, which a formal verification system that uses homotopy type theory (it assumes the univalence axiom).