# 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.

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 limited funding available to support US-based junior participants; 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. 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 the Riemannian and spectral geometry of hyperbolic three-manifolds. 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.
- Monopole Floer homology and invariant theta characteristics.

Accepted/in press:

- 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*.

Here are my list of publications and my Mathscinet profile.

Seminars I co-organize:

## Teaching and Advising

Teaching:- In the Academic Year 2023-24 I am teaching the Graduate Topology sequence.
- A minicourse on Seiberg-Witten theory taught at MSRI in 2021.

- Juan Muñoz-Echániz - Monopoles and Dehn twists on contact 3-manifolds, 2023.
- Alex Xu, 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.