Research

I study 3- and 4-dimensional manifolds using invariants from symplectic geometry and gauge theory.

Publications and Preprints:

  1. Seiberg-Witten knot homology via holonomy filtration (in preparation)

  2. (with Gordana Matic, Jeremy Van Horn-Morris, and Andy Wand) Detecting tightness via spectral order. (in preparation)

  3. (with Gordana Matic, Jeremy Van Horn-Morris, and Andy Wand) Filtering the Heegaard Floer contact invariant. (arXiv)

  4. (with Jonathan Hanselman and Tye Lidman) A remark on the geography problem in Heegaard Floer homology. (arXiv)

  5. (with Gordana Matic, Jeremy Van Horn-Morris, and Andy Wand) Algebraic torsion via Heegaard Floer homology. (arXiv)

  6. (with Steven Sivek) Sutured ECH is a natural invariant, with an appendix by C. H. Taubes. (arXiv)

  7. (with Yi-Jen Lee and Clifford Henry Taubes) HF=HM V: Seiberg-Witten Floer homology and handle addition. (arXiv)

  8. (with Yi-Jen Lee and Clifford Henry Taubes) HF=HM IV: The Seiberg-Witten Floer homology and ech correspondence. (arXiv)

  9. (with Yi-Jen Lee and Clifford Henry Taubes) HF=HM III: Holomorphic curves and the differential for the ech/ Heegaard Floer homology correspondence. (arXiv)

  10. (with Yi-Jen Lee and Clifford Henry Taubes) HF=HM II: Reeb orbits and holomorphic curves for the ech/ Heegaard Floer homology correspondence. (arXiv)

  11. (with Yi-Jen Lee and Clifford Henry Taubes) HF=HM I: Heegaard Floer homology and Seiberg-Witten Floer homology. (arXiv)

  12. 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)

  13. (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, arXiv)

 

Acknowledgements: My work is supported by a Simons Foundation Grant Award No. 519352. In the past, I was supported in part by an NSF MSPRF Award No. DMS-1103795 and an NSF Grant Award No. DMS-1360293.

 

 

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