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).

Teaching: Fall 2025 on leave (topics course at the University of Pisa), Spring 2026 Modern Analysis II.

I am interested in the interactions between geometry and topology, with a focus on gauge theory, Floer homology, hyperbolic manifolds and spectral geometry. I think a lot about the equations of Maxwell and Dirac.

Preprints:

Dirac spectral flow and Floer theory of hyperbolic three-manifolds, with M. Lipnowski (spectral movie).
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).