# Francesco Lin

Assistant Professor of Mathematics at Columbia University (CV, MathGenealogy).

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

Teaching: Fall 2024 Honors Complex Variables (preliminary syllabus here).

## Research

I am interested in geometry and topology in low-dimensions, with a special focus on their mutual interactions. A lot of what I think about originates here. My research is partially supported by the NSF grant *New directions in monopole Floer homology* (DMS-2203498).

I co-organize the Symplectic Geometry and Gauge Theory Seminar and the Geometric Topology seminar.

Preprints:

- Divergence-free framings of three-manifolds via eigenspinors.
- 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.
- Sergey Nersisyan, in progress.

- 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.