My research interests lie at the crossroad of symplectic geometry, gauge theory and low dimensional topology.

An overview of my research aimed at a general audience is available here, and a more detailed research statement is available here.

In preparation, preprints:

  • (in preparation, with Dominic Joyce, Jason Lotay and Alex Ritter) Bridgeland stability for Calabi–Yau 2-folds.
  • (in preparation, with Dominic Joyce and Alex Ritter) A new construction of Fukaya categories for semipositive symplectic manifolds.
  • (in preparation, with Alex Hock and Thibaut Mazuir) A-infinity bialgebras and Hopf algebras.
  • (in preparation, with Paul Kirk, Mike Miller and Wai-Kit Yeung) Equivariant Lagrangian Floer homology via multiplicative flow trees. (talk, slides)
  • Equivariant Lagrangian Floer homology via cotangent bundles of EG_N. Submitted.
  • Accepted, published:

  • (with Chris Herald, Paul Kirk, and Artem Kotelskiy) The correspondence induced on the pillowcase by the earring tangle. To appear in J. Topol. (talk by Artem, talk)
  • A two-category of Hamiltonian manifolds, and a (1+1+1)-field theory. To appear in Indiana Univ. Math. J. (talk)
  • (with Chris Herald, and Paul Kirk) Tangles, relative character varieties, and holonomy perturbed traceless flat moduli spaces. To appear in The Open Book Series. (talk by Chris)
  • Symplectic Instanton Homology: naturality, and maps from cobordisms. Quantum Topol. 10 (2019), no. 4, 677–722.
  • Symplectic Instanton Homology: twisting, connected sums, and Dehn surgery. J. Symplectic Geom. 17 (2019), no. 1, 93–177.
  • Other:

  • PhD. Thesis, Homologie Instanton Symplectique : somme connexe, chirurgie entière, et applications induites par cobordismes. (slides)
  • Some lecture notes for the graduate course I taught at IU in spring 2020 on Fukaya categories. I put them here in case they might be helpful, although these are handwritten and might contain mistakes: use at your own risk!
  • Some slides on a quick introduction to Symplectic Geometry and pseudoholomorphic curves for a preparatory talk to a winter school on Morse/ Floer theory and Fukaya categories I helped to organize.
  • Some slides for a reading seminar on Haydys's paper Fukaya-Seidel category and gauge theory I co-organized with Jason Lotay 1 2 3 4 5 .
  • Slides on Donaldson's diagonalizability theorem (my favorite one): this one was for a colloquium at James Madison University, and was aimed to be accessible to undergraduate students. This other one was for a talk at Oxford's joint geometry and physics junior seminar, and contains more details.