Francesco Lin

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

Office: Department of Mathematics, Room 613.

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

My work is currently supported by the NSF and the Simons Foundation.

Research

I am interested in gauge theory, Floer homology, hyperbolic geometry, spectral theory, and their mutual interactions. I think a lot about the equations of Maxwell and Dirac in three dimensions.

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.

You can find my list of publications here.

Teaching

At Columbia: Fall 2025 on leave, Spring 2026 Modern Analysis II.
An introduction to gauge theory: monopoles and symmetric products, topics course in Pisa.
CRM Montreal lectures: 1 - 2 - 3 - 4.

Last updated 09/25