Papers

• Lagrangian torus invariants using ECH = SWF
  J. Symplectic Geom. 2021
• No homotopy 4-sphere invariants using ECH = SWF
  Algebr. Geom. Topol. 2021
• G2 holonomy, Taubes’ construction of Seiberg-Witten invariants and superconducting vortices
  (with S. Cecotti & C. Vafa), J. High Energy Phys. 2020
• Seiberg-Witten and Gromov invariants for self-dual harmonic 2-forms
  Geom. Topol. 2022 (to appear)
• Taming the pseudoholomorphic beasts in ℝ×(S1×S2)
  Geom. Topol. 2020
• Generic transversality for unbranched covers of closed pseudoholomorphic curves
  (with C. Wendl), Commun. Pure Appl. Math. 2017
• PU(2) monopoles and Casson invariants
  (with A. Doan), preprint to appear

In preparation

• PU(n) monopoles and generalized Witten conjecture. (with A. Doan)
• ….

Notes and unpublished documents

• “Riemann-Roch” for punctured curves. Appendix to PhD thesis, a new proof of the Fredholm index formula for punctured pseudoholomorphic curves.
• Obstruction bundle gluing. Notes from a lecture by Michael Hutchings and a discussion session by myself at the 2015 IHES “moduli” conference.
• Solutions to “Cohomology of Groups”. As an undergraduate I wrote a solutions manual to my mentor Ken Brown’s textbook.
• Essential cohomology of the p-groups with a cyclic subgroup of index p. Unpublished undergraduate research on group cohomology.