Tom Coates

I will describe joint work with Elana Kalashnikov, in which we
systematically construct smooth Fano subvarieties of quiver flag
varieties.  This yields over 100 new four-dimensional Fano manifolds.  I
will explain how this fits into a program -- joint work with Corti, Galkin,
Golyshev, Kasprzyk, and others -- to find and classify Fano manifolds using
mirror symmetry.