I am a postdoctoral researcher at the University of Helsinki, working in low-dimensional topology.
- 2024–2027University of Helsinki, Postdoctoral Researcher (supervisor Kari Vilonen, research mentor Oscar Kivinen, Aalto University)
- 2021–2024University of Southern Denmark, Center for Quantum Mathematics, Postdoctoral Researcher (mentor Vivek Shende)
- 2021Ph.D. in Mathematics, UCLA (advisor Ciprian Manolescu)
- 2015B.S. in Mathematics and B.S. in Physics, Stanford University
Teaching
- Autumn 2026Algebra IIb: Rings, Modules, and Galois Theory · University of Helsinki
- Spring 2026Algebraic Topology · University of Helsinki
- Spring 2024Topology and Complex Analysis · University of Southern Denmark
- Spring 2023Topology and Complex Analysis · University of Southern Denmark
- 2015–2019Teaching assistant, UCLA · Linear Algebra and Applications, Differential Equations, Algebraic Topology, Differential Geometry, Differential Topology
Students
- 2026–2027Alexander Saunders, master's student, University of Helsinki
- Autumn 2026Cristian Ionita, bachelor's thesis, Aalto University · Khovanov homology and the Rasmussen s-invariant
Research
I am interested in algebraic invariants in low-dimensional topology. I have worked on the skein lasagna module, which is a 4-manifold invariant built from Khovanov homology, and sheaf-theoretic SL(2, ℂ) Floer homology.
Papers
- 2023SL(2, ℂ) Floer homology for surgeries on some knots. Michigan Math. J. arXiv:2002.04103
- 2022Skein lasagna modules for 2-handlebodies (with Ciprian Manolescu). J. Reine Angew. Math. arXiv:2009.08520
- 2022On the sheaf-theoretic SL(2, ℂ) Casson–Lin invariant (with Laurent Côté). J. Math. Soc. Japan. arXiv:1907.02593
Seminars
Learning seminars organized at the University of Southern Denmark.
- Spring 2024Seiberg–Witten invariants
- Spring 2024Methods of classical homotopy theory
- 2022–2023Floer homology and the Fukaya category
- 2022–2023Microlocal sheaf theory: the Tamarkin category (with Bingyu Zhang)
- 2021–2022Introduction to J-holomorphic curves