# Francesco Lin

Associate Professor at Columbia University. CV and MathGenealogy.

Office: Department of Mathematics 613.

Email: flin-at-math.columbia.edu (research), fl2550-at-columbia.edu (teaching).

Teaching: Fall 2024 Honors Complex Variables, Spring 2025 Modern Analysis II.

## Research

I am interested in geometry, topology and their mutual interactions. I think a lot about three-manifolds, Floer theory, spinors, hyperbolic geometry and spectra of operators. I co-organize the Columbia Geometric Topology seminar. My work is partially supported by the NSF grant *New directions in monopole Floer homology* (DMS-2203498).

Preprints:

- On integral rigidity in Seiberg-Witten theory, with M. Miller Eismeier.
- Divergence-free framings of three-manifolds via eigenspinors.
- Topology of the Dirac equation on spectrally large three-manifolds.
- Homology cobordism and the geometry of hyperbolic three-manifolds.

- A remark on taut foliations and Floer homology,
*Mathematical Research Letters*. - 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:- Sergey Nersisyan and Alex Xu, in progress.
- Juan Muñoz-Echániz - Monopoles and Dehn twists on contact 3-manifolds, 2023.

I am a faculty advisor for the Columbia Journal of Undergraduate Mathematics.

Undergraduate research projects:

- Anda Tenie - Strongly isospectral hyperbolic three-manifolds with nonisomorphic rational cohomology rings.

*"...il voler trattar le quistioni naturali senza geometria è un tentar di fare quello che è impossibile ad esser fatto."*

G. Galilei - Dialogo sopra i due massimi sistemi del mondo.