Francesco Lin

Research

I am interested in geometry, topology and their mutual interactions. I think a lot about three-manifolds, Floer theory, hyperbolic geometry and the equations of Maxwell and Dirac. My work is partially supported by the NSF grant New directions in monopole Floer homology (DMS-2203498). I co-organize the Columbia Geometric Topology seminar.

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

• Sergey Nersisyan and Alex Xu, in progress.
• Juan Muñoz-Echániz - Monopoles and Dehn twists on contact 3-manifolds, 2023.

• Anda Tenie - Strongly isospectral hyperbolic three-manifolds with nonisomorphic rational cohomology rings.

I am a faculty advisor for the Columbia Journal of Undergraduate Mathematics and the Econ-Math major.