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. My work is currently supported by the NSF grant New directions in monopole Floer homology (DMS-2203498).

Last updated 06/25