Francesco Lin

I am interested in geometry, topology and analysis, especially in low dimensions. Specifically, I work on gauge theory, Floer homology and hyperbolic geometry, with an emphasis on trying to understand their mutual interactions in concrete examples. I think a lot about the equations of Maxwell and Dirac.

Publication list and preprints:

• Coexact 1-form spectral gaps of hyperbolic rational homology spheres, with M. Lipnowski (spectral movie).
• 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, Annales de l'Institut Fourier.

Preliminary notes for an introductory graduate-level textbook on gauge theory and topology.

My MathGenealogy. Current PhD students: Charlotte Máthé, Sergey Nersisyan, Felix Roz.

I am an editor at Mathematical Research Letters.

• Spring 2027: MATH GR6308 Algebraic Topology II.
• Fall 2026: MATH GU4065 Honors Complex Variables.

• Symplectic Geometry, Gauge Theory and Topology.
• (Informal) Low-dimensional Topology.