Francesco Lin

Research

I am interested in gauge theory, Floer homology, low-dimensional topology, hyperbolic geometry and spectra of elliptic operators, with a focus on their mutual interactions. A lot of what I think about originates here.

My research is partially supported by the NSF grant New directions in monopole Floer homology (DMS-2203498).

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

Preprints:

• Divergence-free framings of three-manifolds via eigenspinors.
• Topology of the Dirac equation on spectrally large three-manifolds.
• A remark on taut foliations and Floer homology.
• Homology cobordism and the geometry of hyperbolic three-manifolds.

• Lectures on families of Dirac operators and applications (expository), Proceedings of the Mrowkafest (PSPM).
• Monopole Floer homology and invariant theta characteristics, Journal of the LMS.
• Monopoles, twisted integral cohomology, and Hirsch algebras, with M. Miller Eismeier, Geometry & Topology.
• Closed geodesics and Frøyshov invariants of hyperbolic three-manifolds, with M. Lipnowski, Journal of the EMS.

Advising

• Juan Muñoz-Echániz - Monopoles and Dehn twists on contact 3-manifolds, 2023. Now at SCGP.
• Alex Xu, in progress.
• Sergey Nersisyan, in progress.

• Anda Tenie - Strongly isospectral hyperbolic three-manifolds with nonisomorphic rational cohomology rings.