Francesco Lin

Research

I am interested in low-dimensional topology, differential geometry and global analysis, with a special emphasis on their mutual interactions. Most of my work involves the Seiberg-Witten equations and Floer homology; lately I have been focusing on their relation to the Riemannian and spectral geometry of hyperbolic three-manifolds.
My research is partially supported by NSF grant DMS-2203498.

Preprints:

• A remark on taut foliations and Floer homology.
• Homology cobordism and the geometry of hyperbolic three-manifolds.
• Monopole Floer homology and invariant theta characteristics.

Accepted/in press:

• Lectures on families of Dirac operators and applications (expository), Proceedings of the Mrowkafest (PSPM).
• 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.

Here are my list of publications and my Mathscinet profile.

Teaching and Advising

In the Academic Year 2023-24 I am teaching the Graduate Topology sequence.

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

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

Seminars

• Columbia Symplectic Geometry and Gauge Theory Seminar.
• Columbia Geometric Topology seminar.