Amanda Hirschi


Properties of Gromov-Witten invariants defined via global Kuranishi charts
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
joint 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 become deformation equivalent after one stabilisation have the same Gromov-Witten invariants.

Infinitely many monotone Lagrangian tori in higher projective spaces
joint with Soham Chanda and Luya Wang, submitted
We construct infinitely many exotic tori in all higher projective spaces by lifting the Vianna tori from the projective plane and showing that the lifts remain non-symplectomorphic.

Global Kuranishi charts and a product formula in symplectic Gromov-Witten theory joint with Mohan Swaminathan, submitted
We construct a global Kuranishi chart for moduli space of stable pseudoholomorphic maps of arbitrary genus.  We use this presentation to prove a product formula in symplectic Gromov-Witten theory.

Lagrangian intersections and cuplength in generalised cohomology
joint with Noah Porcelli, accepted for publication in Mathematical Research Letters
Using generalised cohomology theories we find better lower bounds on the number of intersection points of two Lagrangians in the absence of transversality conditions.


Flow categories
Notes taken during the Floer homotopy theory summer school in Vancouver