Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

SYZ Mirror Symmetry and Optimal Transport on Polytopes

A long-standing conjecture motivated by Mirror Symmetry predicts that Calabi-Yau manifolds close to large complex structure limits admit special Lagrangian torus fibrations. A recent breakthrough reduces a weak version of this conjecture to a PDE problem in a tropical setting. I will explain some of this and how optimal transport theory fits well into this PDE problem. In particular, I will present results concerning a setting of hypersurfaces in toric Fano manifolds, where the PDE problem is set on the boundary of a polytope. This is based on joint work with Rolf Andreasson, Mattias Jonsson, Enrica Mazzon and Nick McCleerey.