Titles and abstracts

Monday 23 March  10.00 am  

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. 

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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.