I am an Assistant Professor at the Department of Mathematics of Columbia University.
My email addresses are flin-at-math-dot-columbia-dot-edu (research) and fl2550-at-columbia-dot-edu (teaching).
I am interested in low-dimensional topology, global analysis, and their interactions. Most of my work involves the Seiberg-Witten equations and Floer homology; lately I have been thinking about the geometry of Riemann surfaces and hyperbolic three-manifolds. My research is partially supported by the Alfred P. Sloan Foundation and NSF grant DMS-2203498.
- Homology cobordism and the geometry of hyperbolic three-manifolds.
- Lectures on families of Dirac operators and applications, submitted (expository notes).
- Monopole Floer homology and invariant theta characteristics, submitted.
- Monopoles, twisted integral cohomology, and Hirsch algebras, with Mike Miller Eismeier, submitted.
- Closed geodesics and Frøyshov invariants of hyperbolic three-manifolds, with Michael Lipnowski, submitted.
Seminars I co-organize:
Mentoring and teachingCurrent PhD Students:
- Anda Tenie - Strongly isospectral hyperbolic three-manifolds with nonisomorphic rational cohomology rings, independent summer project 2021, submitted.
- Spring 2023: Intro to Higher Mathematics.
- In Fall 2022: Honors Complex Variables.
- Patrick Lei took live notes for the Spring 2021 graduate class Algebraic Topology II.