Francesco Lin

Associate Professor at Columbia University. My CV.

Office: Department of Mathematics, Room 613.

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

My research lies at the interface between low-dimensional topology and geometric analysis. Specifically, I am interested in gauge theory, Floer homology, hyperbolic geometry and spectral theory, with an emphasis on trying to understand their mutual interactions in concrete examples. I think a lot about the equations of Maxwell and Dirac.

Publication list and preprints:

Coexact 1-form spectral gaps of hyperbolic rational homology spheres, with M. Lipnowski (spectral movie).
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, Annales de l'Institut Fourier.

Preliminary notes for an introductory graduate-level textbook on gauge theory and topology.

PhD students:

Current: Charlotte Máthé, Sergey Nersisyan, Felix Roz.
Alex Xu - The Seiberg-Witten equations and asymptotically hyperbolic Einstein metrics (2025).
Juan Muñoz-Echániz - Monopoles and Dehn twists on contact three-manifolds (2023).

Teaching:

Spring 2027: MATH GR6308 Algebraic Topology II.
Fall 2026: MATH GU4065 Honors Complex Variables.

Activities:

I am an editor at Mathematical Research Letters.
Symplectic Geometry, Gauge Theory and Topology seminar.

Last updated 08/26