Francesco Lin
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).
Here are my CV and MathGenealogy.
Combinatorial and gauge theoretical methods in low-dimensional topology and geometry in Pisa, June 3-7 2024.
Research
I am interested in low-dimensional topology, differential geometry and global analysis, with a special emphasis on their interplay in dimension three. I like to think about these topics from the perspective of the Seiberg-Witten equations and the associated Floer theoretic invariants. Lately I have been exploring interactions with Riemannian geometry and spectral theory. It all started with these. My research is partially supported by the NSF grant DMS-2203498.
I co-organize the Symplectic Geometry and Gauge Theory Seminar and the Geometric Topology seminar.
Preprints:
- Topology of the Dirac equation on spectrally large three-manifolds.
- A remark on taut foliations and Floer homology.
- Homology cobordism and the geometry of hyperbolic three-manifolds.
- Lectures on families of Dirac operators and applications (expository), Proceedings of the Mrowkafest (PSPM).
- Monopole Floer homology and invariant theta characteristics, Journal of the LMS.
- 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.
Advising
PhD Students:- Juan Muñoz-Echániz - Monopoles and Dehn twists on contact 3-manifolds, 2023. Now at SCGP.
- Alex Xu, in progress.
- Anda Tenie - Strongly isospectral hyperbolic three-manifolds with nonisomorphic rational cohomology rings.