Classification problems and mirror duality

We report on the progress of a program that aims at classifying Fano varieties
(or Fano-like objects) by the tools and methods of mirror symmetry.

Attention : il y a un 2d expose au séminaire de la théorie des nombres, le mercredi 27 janvier a 14h, la salle 04 :

Apery constants of homogeneous varieties.

We interpret the differential equations considered by Apery as quantum differential equations of certain Fano varieties. For more complicated topologies one obtains differential equations that yield simultaneous approximations to a number of zeta values. We compute the Apery constants for Fano threefolds and relate them to their birational types.