Francesco Lin

Research

I am interested in low-dimensional topology, geometric analysis, and their interactions. Most of my work involves the Seiberg-Witten equations and Floer homology. My research is partially supported by the Alfred P. Sloan Foundation and NSF grant DMS-2203498.

I co-organize the Columbia Symplectic Geometry, Gauge Theory, and Categorification Seminar and the Columbia Geometric Topology seminar.

Preprints:

• Lectures on families of Dirac operators and applications, 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.

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.

• Families of Dirac operators and applications, 2022 ICTP Summer School Frontiers in Geometry and Topology.
• An introduction to Seiberg-Witten invariants, 2021 MSRI Summer School Gauge Theory in Geometry and Topology.

• In Fall 2022, I am teaching Honors Complex Variables.
• Patrick Lei took live notes for the Spring 2021 graduate class Algebraic Topology II.