Francesco Lin

Associate Professor of Mathematics at Columbia University. My CV and MathGenealogy.

Office: Mathematics 613.

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

I will be on leave in Fall 2025. Among the other things, I will teach a topics course at the University of Pisa.

In Spring 2026, I will teach Modern Analysis II.

I am interested in the interplay between geometry and topology, with a focus on low-dimensional topology, Floer homology, hyperbolic manifolds, spectral geometry and the equations of Maxwell and Dirac.

Preprints:

Adjunction inequalities and the Davis hyperbolic four-manifold, with B. Martelli.
On integral rigidity in Seiberg-Witten theory, with M. Miller Eismeier.
Topology of the Dirac equation on spectrally large three-manifolds.

In press/to appear:

Divergence-free framings of three-manifolds via eigenspinors, Documenta Mathematica.
Closed geodesics and Frøyshov invariants of hyperbolic three-manifolds, with M. Lipnowski, Journal of the EMS.

You can find my list of publications here. I co-organize the Columbia Geometric Topology seminar. My work is currently supported by the NSF grant New directions in monopole Floer homology (DMS-2203498).