Francesco Lin

Associate Professor of Mathematics at Columbia University. CV and MathGenealogy.

Office: Department of Mathematics, Room 613.

Email: flin-at-math.columbia.edu (research), fl2550-at-columbia.edu (teaching).

My work is currently supported by the grants NSF DMS-2503714 and Simons Foundation TSM-00013131.

Notes for the course Gauge theory and topology - an introduction in Pisa:

Lecture 1 - From magnetostatics to gauge theory.
Lecture 2 - Curvature and characteristic classes.
Lecture 3 - Yang-Mills theory on Riemannian manifolds.
Lecture 4 - Instantons, monopoles, vortices.
Lecture 5 - Elliptic operators and Sobolev spaces.
Lecture 6 - The Hodge theorem and index theory.

I am interested in the interplay between geometry, topology and analysis in low dimension, with a focus on Floer homology, hyperbolic geometry and spectral theory. I think a lot about the equations of Maxwell and Dirac.

Publication list and preprints:

Dirac spectral flow and Floer theory of hyperbolic three-manifolds, with M. Lipnowski (spectral movie).
Adjunction inequalities and the Davis hyperbolic four-manifold, with B. Martelli.
Divergence-free framings of three-manifolds via eigenspinors, Documenta Mathematica.
Topology of the Dirac equation on spectrally large three-manifolds.

Last updated 11/25