Preprints
An open-closed Deligne-Mumford field theory associated to a Lagrangian submanifold
with Kai Hugtenburg
Using global Kuranishi charts for moduli spaces of stable maps with Lagrangian boundary condition, we construct an open-closed Deligne-Mumford field theory associated to a closed relatively spin Lagrangian. Among other things, this yields a chain-level lift of Gromov-Witten theory.
Properties of Gromov-Witten invariants defined via global Kuranishi charts
accepted for publication in Annales Henri Lebesgue
We prove that the Gromov-Witten invariants constructed by Hirschi-Swaminathan satisfy the Kontsevich-Manin axioms. The construction extends to the equivariant setting and we prove a localisation formula for the equivariant Gromov-Witten invariants of certain Hamiltonian torus manifolds.
On Donaldson’s 4-6 question
with Luya Wang, submitted
We prove that the examples of Smith and McMullen-Taubes provide infinitely many counterexamples to one direction of the Donaldson four-six question and the closely related Stabilising Conjecture. In the other direction we show that manifolds that be-
come deformation equivalent after one stabilisation have the same Gromov-Witten invariants.
Articles
Lagrangian intersections and cuplength in generalised cohomology
with Noah Porcelli
Mathematical Research Letters, Vol. 32, Issue 1 (2025)
Infinitely many monotone Lagrangian tori in higher projective spaces
with Soham Chanda and Luya Wang
J. Fixed Point Theory Appl. 26, 46 (2024)
Global Kuranishi charts and a product formula in symplectic Gromov-Witten theory with Mohan Swaminathan
Selecta Math. (N.S) 30, 87 (2024)
Notes
Flow categories
Notes taken during the Floer homotopy theory summer school in Vancouver