Francesco Lin

Associate Professor at Columbia University (CV, MathGenealogy).

Office: Department of Mathematics, Room 613.

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

I am interested in the interplay between geometry, topology and analysis in low dimension. I spend a lot of time thinking about the equations of Maxwell and Dirac on three-manifolds, especially hyperbolic ones.

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.
Topology of the Dirac equation on spectrally large three-manifolds, Journal of the IMJ.

My work is currently supported by the grants NSF DMS-2503714 and Simons Foundation TSM-00013131.

Teaching:

Spring 2026 - Modern Analysis II.
Fall 2025 - Gauge theory and topology, topics course in Pisa (notes).

I co-organize the Symplectic Geometry, Gauge Theory, and Categorification seminar.

Last updated 03/26