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.
I co-organize the Symplectic Geometry and Gauge Theory Seminar and the Geometric Topology seminar.
We are organizing the conference Combinatorial and gauge theoretical methods in low-dimensional topology and geometry, to be held at CRM De Giorgi (Pisa, Italy) on June 3rd-7th 2024. There is funding available for US-based junior participants provided by the NSF conference grant DMS-2349401; you can find the relevant information here.
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 and spectral geometry, especially in the case of hyperbolic three-manifolds. It all started with these.
My research is partially supported by the NSF grant New directions in monopole Floer homology (DMS-2203498).
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 and Teaching
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.
- In the Academic Year 2023-24 I am teaching the Graduate Topology sequence.
- A minicourse on Seiberg-Witten theory taught at MSRI in 2021.