# 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.

## Research

I am interested in low-dimensional topology, differential geometry and global analysis, with a special emphasis on their mutual interactions. Most of my work involves the Seiberg-Witten equations and Floer homology; lately I have been focusing on their relation to the Riemannian and spectral geometry of hyperbolic three-manifolds.

My research is partially supported by NSF grant DMS-2203498.

Preprints:

- A remark on taut foliations and Floer homology.
- Homology cobordism and the geometry of hyperbolic three-manifolds.
- Monopole Floer homology and invariant theta characteristics.
- Closed geodesics and Frøyshov invariants of hyperbolic three-manifolds, with Michael Lipnowski.

In press:

- Lectures on families of Dirac operators and applications (expository),
*Proceedings of the Mrowkafest (PSPM)*. - Monopoles, twisted integral cohomology, and Hirsch algebras, with Mike Miller Eismeier,
*Geometry & Topology*.

Here are my list of publications and my Mathscinet profile.

## Teaching and Advising

In the Academic Year 2023-24 I am teaching the Graduate Topology sequence.

PhD Students:

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

## Seminars

## Past events

- Geometric Topology in NY 2023.
- A minicourse on Seiberg-Witten theory taught at MSRI in 2021.