For the first semester of 2025-2026, the seminar will run on Fridays, 13:00 to 14:00. On September 5, the room is Lecture Theatre A. Afterwards, room TBD.
September 5: Amanda Hirschi (Sorbonne)
On stabilisations of symplectic 4-manifolds
Two simply-connected smooth 4-manifolds are homeomorphic if and only if their stabilisations, i.e. products with S^2, are diffeomorphic. The Donaldson 4-6 question asks whether this fact can be lifted to the symplectic category. It asks whether the underlying smooth manifolds of two (simply-connected) symplectic manifolds are diffeomorphic if and only if their products with S^2, equipped with the standard area form, are symplectic deformation equivalent. I will describe one example of a smooth 4-manifold admitting two symplectic forms that remain deformation inequivalent after taking the product with S^2, giving counterexamples to one implication of the conjecture. On the other hand, I will explain why two symplectic manifolds, whose stabilisations are deformation equivalent, have the same Gromov-Witten invariants. This is joint work with Luya Wang.Â
September 19: Violeta Lopez (St Andrews)
September 26: Alison La Porta (St Andrews)
October 3: TBD
October 10: Ben Martin (Aberdeen)
October 17: Diane Maclagan (Warwick)
October 24: TBD
October 31: Rachael Boyd (Glasgow)
November 7: Aporva Varshney (UCL)