# Francesco Lin

I am an Assistant Professor at the Department of Mathematics of Columbia University.

My email addresses are flin-at-math-dot-columbia-dot-edu (research) and fl2550-at-columbia-dot-edu (teaching).

Here are my CV and MathGenealogy.

## 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

Current PhD Students: Undergraduate research supervised:- 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.

This page was last updated in September 2022.