Valentino Tosatti

I will discuss the behavior of Ricci-flat K\"ahler metrics on the
total space of a fibration in the adiabatic limit when the volume of the
fibers shrinks to zero. On the geometric side, this problem is relevant
for the Strominger-Yau-Zaslow picture of mirror symmetry. On the analytic
side, it is equivalent to studying solutions of a degenerating family
of complex Monge-Ampere equations.