Titles and abstracts

Monday 23 March  

10.00am Jonny Evans (Lancaster)  

Isotopy uniqueness for pin-ellipsoids 

Pin-ellipsoids are a class of symplectic domains which generalise standard symplectic ellipsoids. They arise as Milnor fibres of cyclic quotient T-singularities. There are many interesting pin-ellipsoids inside the complex projective plane, coming from the ways it can degenerate to a weighted projective space. We will show that any symplectic pin-ellipsoid in CP^2 is isotopic to one coming from an algebraic degeneration. Based on joint work with Nikolas Adaloglou, Joé Brendel, Johannes Hauber and Felix Schlenk and builds upon and illuminates earlier joint work with Ivan Smith. 

4.00-5.00 Marcelo Atallah (Sheffield)

C⁰-rigidity of the Hamiltonian diffeomorphism group of symplectic rational surfaces

A natural question bridging the celebrated Gromov–Eliashberg theorem and the C⁰-flux conjecture is whether the identity component of the group of symplectic diffeomorphisms is C⁰-closed in Symp(M,ω). Beyond surfaces and the cases in which the Torelli subgroup of Symp(M,ω) coincides with the identity component, little is known. In joint work with Cheuk Yu Mak and Wewei Wu, we show that, for all but a few positive rational surfaces, the group of Hamiltonian diffeomorphisms is the C⁰-connected component of the identity in Symp(M,ω), thereby giving a positive answer in this setting. Here, “positive rational surface” essentially means a k-point blow-up of CP² whose symplectic form evaluates positively on the first Chern class. 

Tuesday  24th March

4.00pm  Amanda Hirschi (Sorbonne, Paris)

String-valued open Gromov--Witten invariants

I will discuss joint work in progress with Yash Deshmukh in which we construct a geometrically defined model for the homotopy involutive bi-Lie algebra structure on reduced S^1-equivariant chains on the free loop space of an arbitrary smooth closed manifold. We define a higher genus open Gromov--Witten potential of a closed Lagrangian brane valued in the involutive bi-Lie algebra of the reduced equivariant chains on the free loop space of the Lagrangian, realizing a proposal of Cieliebak--Fukaya--Latschev. 

Wednesday 25th March

Thursday 26th March 

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Friday  27th March 11.00

11.00am Cheuk Yu Mak (Sheffield)

Lagrangian torus fibration on Calabi-Yau hypersurfaces

In joint work with Matessi-Ruddat-Zharkov, we prove the existence of Lagrangian torus fibrations on Calabi-Yau hypersurfaces in toric Fano manifolds given by a reflexive polytope. The result is motivated by the Strominger-Yau-Zaslow conjecture, which predicts the existence of these fibrations on Calabi-Yau manifolds near large complex structure limits. In this talk, I will outline the main setup of the construction. The idea is to replace the ordinary algebraic equation with a new one involving "ironing coefficients" and a convex (but not strictly convex!) potential which has the effect of breaking the manifold into local models. Over these models, we apply the Liouville flow technique in the style of Evans-Mauri.