Francesco Lin

Research

I am interested in low-dimensional topology, global analysis, and their interactions. Most of my work involves the Seiberg-Witten equations and Floer homology; lately I have been thinking about the geometry of Riemann surfaces and hyperbolic three-manifolds. My research is partially supported by the Alfred P. Sloan Foundation and NSF grant DMS-2203498.

Preprints:

• Homology cobordism and the geometry of hyperbolic three-manifolds.
• Lectures on families of Dirac operators and applications, submitted (expository notes).
• Monopole Floer homology and invariant theta characteristics, submitted.
• Monopoles, twisted integral cohomology, and Hirsch algebras, with Mike Miller Eismeier, submitted.
• Closed geodesics and Frøyshov invariants of hyperbolic three-manifolds, with Michael Lipnowski, submitted.

Here are my list of publications and Mathscinet profile.

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

Mentoring and teaching

• Juan Muñoz-Echániz.
• Alex Xu.

• Anda Tenie - Strongly isospectral hyperbolic three-manifolds with nonisomorphic rational cohomology rings, independent summer project 2021, submitted.

• Spring 2023: Intro to Higher Mathematics.
• In Fall 2022: Honors Complex Variables.
• Patrick Lei took live notes for the Spring 2021 graduate class Algebraic Topology II.