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, differential geometry and global analysis, with a special emphasis on their mutual interactions. Most of my work involves the Seiberg-Witten equations and Floer homology; lately I have been focusing on their relation to the Riemannian and spectral geometry of hyperbolic three-manifolds. My research is partially supported by NSF grant DMS-2203498.
- A remark on taut foliations and Floer homology.
- Homology cobordism and the geometry of hyperbolic three-manifolds.
- Monopole Floer homology and invariant theta characteristics.
- Lectures on families of Dirac operators and applications (expository), Proceedings of the Mrowkafest (PSPM).
- Monopoles, twisted integral cohomology, and Hirsch algebras, with M. Miller Eismeier, Geometry & Topology.
- Closed geodesics and Frøyshov invariants of hyperbolic three-manifolds, with M. Lipnowski, Journal of the EMS.
Teaching and Advising
In the Academic Year 2023-24 I am teaching the Graduate Topology sequence.PhD Students:
- Juan Muñoz-Echániz - Monopoles and Dehn twists on contact 3-manifolds, 2023.
- Alex Xu, in progress.