# Francesco Lin

Hi! I am an Assistant Professor at the Columbia Department of Mathematics. Here is my CV. My email address is flin-at-math-dot-columbia-dot-edu.

## Research

My work lies at the intersection between low-dimensional topology, geometry, and elliptic PDEs; most of it involves the Seiberg-Witten equations on three-manifolds. My research is supported by the NSF and the Alfred P. Sloan Foundation.

Preprints:

- Indefinite Stein fillings and Pin(2)-monopole Floer homology

Submitted. - Monopole Floer homology and SOLV geometry

Submitted. - Hyperbolic four-manifolds with vanishing Seiberg-Witten invariants

with Ian Agol, submitted. - The Seiberg-Witten equations and the length spectrum of hyperbolic three-manifolds

with Michael Lipnowski, submitted. - Non-formality in Pin(2)-monopole Floer homology

Submitted.

Publications:

- Pin(2)-monopole Floer homology and the Rokhlin invariant

*Compositio Mathematica*154 (2018), no. 12, 2681-2700. - Monopole Floer homology and the spectral geometry of three-manifolds

Accepted for publication in*Communications in Analysis and Geometry*. - Bar-Natan's deformation of Khovanov homology and involutive monopole Floer homology

*Mathematische Annalen*373 (2019) no. 1-2, 489-516. - Pin(2)-monopole Floer homology, higher compositions and connected sums

*Journal of Topology*10 (2017), no. 4, 921-969. - The surgery exact triangle in Pin(2)-monopole Floer homology

*Algebraic & Geometric Topology*17-5 (2017), 2915--2960. - Exact Lagrangian caps of Legendrian knots

*Journal of Symplectic Geometry*, Vol. 14, No. 1 (2016), pp. 269-295.

Monographs:

- A Morse-Bott approach to monopole Floer homology and the Triangulation conjecture

*Memoirs of the AMS*, 255 (2018), no. 1221. With Errata.

Expository writings:

- Lecture notes on monopole Floer homology

*Proceedings of the 22nd Gokova Geometry/Topology conference*(2016), pp. 39-80. - Bordered Heegaard Floer homology

This is my Master's thesis. You can blame the me from the past if you find mistakes.

## Teaching

Here's some graduate level classes I have taught:- Spring 2020: Algebraic Topology II.
- Spring 2019: Topics in Topology: Elliptic operators and Topology.