Francesco Lin
Associate Professor of Mathematics at Columbia University. CV and MathGenealogy.
Email: flin-at-math.columbia.edu (research), fl2550-at-columbia.edu (teaching).
Teaching: Fall 2024 Honors Complex Variables (preliminary syllabus), Spring 2025 Modern Analysis II.
Research
I am interested in geometry and topology in low-dimensions, with a special focus on understanding their mutual interactions using analytic tools. My research is partially supported by NSF grant DMS-2203498.
Preprints:
- Divergence-free framings of three-manifolds via eigenspinors.
- Topology of the Dirac equation on spectrally large three-manifolds.
- Homology cobordism and the geometry of hyperbolic three-manifolds.
- A remark on taut foliations and Floer homology, Mathematical Research Letters.
- Lectures on families of Dirac operators and applications (expository), Proceedings of the Mrowkafest (PSPM).
- Monopole Floer homology and invariant theta characteristics, Journal of the LMS.
- 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:- Juan Muñoz-Echániz - Monopoles and Dehn twists on contact 3-manifolds, 2023. Now at SCGP.
- Alex Xu, in progress.
- Sergey Nersisyan, in progress.
- 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.