# 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.

Some announcements:

- We are hosting the conference Geometric Topology in NY at Columbia University on June 2-4.
- Next year I will teach the first year graduate level Topology sequence. You can find a preliminary syllabus here.

## Research

I am interested in low-dimensional topology, differential geometry, global analysis, and their interactions. Most of my work involves the Seiberg-Witten equations and Floer homology; lately I have been thinking about the geometry of hyperbolic three-manifolds.

My research is partially supported by the Alfred P. Sloan Foundation and NSF grant DMS-2203498.

Preprints:

- Homology cobordism and the geometry of hyperbolic three-manifolds, submitted.
- Lectures on families of Dirac operators and applications (expository notes),

to appear in*Proceedings of the Mrowkafest (PSPUM)*. - Monopole Floer homology and invariant theta characteristics, submitted.
- Monopoles, twisted integral cohomology, and Hirsch algebras,

with Mike Miller Eismeier, to appear in*Geometry & Topology*. - Closed geodesics and Frøyshov invariants of hyperbolic three-manifolds,

with Michael Lipnowski, submitted.

Here are my list of publications and Mathscinet profile.

## Advising

PhD Students:- Juan Muñoz-Echániz has recently defended his thesis
*Monopoles and Dehn twists on contact 3-manifolds*. - Alex Xu, third year.

- Anda Tenie - Strongly isospectral hyperbolic three-manifolds with nonisomorphic rational cohomology rings, summer 2021, submitted.

## Seminars

This page was last updated in May 2023.