Francesco Lin
Associate Professor at Columbia University. My CV.
Office: Department of Mathematics 613.
Email: flin-at-math.columbia.edu (research), fl2550-at-columbia.edu (teaching).
Teaching: Fall 2024 Honors Complex Variables, Spring 2025 Modern Analysis II.
Research
I am interested in geometry, topology and their mutual interactions. I think a lot about three-manifolds, Floer theory, spinors, hyperbolic geometry and spectra of operators. I co-organize the Columbia Geometric Topology seminar. My work is partially supported by the NSF grant New directions in monopole Floer homology (DMS-2203498).
Preprints:
- On integral rigidity in Seiberg-Witten theory, with M. Miller Eismeier.
- Topology of the Dirac equation on spectrally large three-manifolds.
- Homology cobordism and the geometry of hyperbolic three-manifolds.
- Divergence-free framings of three-manifolds via eigenspinors, Documenta Mathematica.
- A remark on taut foliations and Floer homology, Mathematical Research Letters.
- Monopoles, twisted integral cohomology, and Hirsch algebras, with M. Miller Eismeier, Geometry & Topology.
- Closed geodesics and Frøyshov invariants of hyperbolic three-manifolds, with M. Lipnowski, Journal of the EMS.
Advising
PhD Students:- Sergey Nersisyan and Alex Xu, in progress.
- Juan Muñoz-Echániz - Monopoles and Dehn twists on contact 3-manifolds, 2023.
I am a faculty advisor for the Columbia Journal of Undergraduate Mathematics.
Undergraduate research projects:- Anda Tenie - Strongly isospectral hyperbolic three-manifolds with nonisomorphic rational cohomology rings.
"...il voler trattar le quistioni naturali senza geometria è un tentar di fare quello che è impossibile ad esser fatto."
G. Galilei - Dialogo sopra i due massimi sistemi del mondo.