PhD, University of Michigan

Low-dimensional topology, contact and symplectic geometry, gauge theory.

My research interests are in the geometry and topology of low-dimensional manifolds. Invariants of low-dimensional manifolds from gauge theory and symplectic geometry are at the center of my research.

(with Steven Sivek) Sutured ECH is a natural invariant, with an appendix by C. H. Taubes. To appear in Memoirs of the American Mathematical Society. (arXiv)

(with Yi-Jen Lee and Clifford Henry Taubes) HF=HM V: Seiberg-Witten Floer homology and handle addition, Geom. Topol.  24 (2020), no. 7, 3470--3748. (Published version)

(with Yi-Jen Lee and Clifford Henry Taubes) HF=HM IV: The Seiberg-Witten Floer homology and ech correspondence, Geom. Topol.  24 (2020), no. 7, 3219--3469. (Published version)

(with Yi-Jen Lee and Clifford Henry Taubes) HF=HM III: Holomorphic curves and the differential for the ech/Heegaard Floer homology correspondence, Geom. Topol. 24 (2020), no. 6, 3013--3218. (Published version)

(with Yi-Jen Lee and Clifford Henry Taubes) HF=HM II: Reeb orbits and holomorphic curves for the ech/Heegaard Floer homology correspondence, Geom. Topol. 24 (2020), no. 6, 2855--3012. (Published version)

(with Yi-Jen Lee and Clifford Henry Taubes) HF=HM I: Heegaard Floer homology and Seiberg-Witten Floer homology, Geom. Topol. 24 (2020), no. 6, 2829--2854. (Published version)

Lectures on the equivalence of Heegaard Floer and Seiberg-Witten Floer homologies, Proceedings of the Gokova Geometry-Topology Conference 2012, 1-42, Int. Press, Somerville, MA, 2013. (Published version)

(with Clifford Henry Taubes) Seiberg-Witten Floer homology and symplectic forms on S^1 x M^3, Geom. Topol. 13 (2009), no. 1, 493--525. (Published version)