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 work is currently supported by the grants NSF DMS-2503714 and Simons Foundation TSM-00013131.
I am interested in the interplay between geometry, topology and analysis in low dimension. More specifically, I work on gauge theory and Floer homology; I spend a lot of time thinking about the equations of Maxwell and Dirac on Riemannian three-manifolds, with a focus on concrete examples (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, Annales de l'Institut Fourier.
- Topology of the Dirac equation on spectrally large three-manifolds, Journal of the IMJ.
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).
- Spring 2027 - Algebraic Topology II.
- Fall 2026 - Honors Complex Variables.
- Spring 2026 - Modern Analysis II.
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Teaching:
Last updated 04/26