Abstract: Quartic double solids and Gushel-Mukai threefolds are examples of prime
Fano threefolds known to share many numerical properties. In the talk I will explain
how one can construct a smooth and proper over the base family of triangulated categories
with special fiber the nontrivial component of the derived category of a quartic double solid
and general fiber the nontrivial component of the derived category of a Gushel-Mukai threefold.
As a consequence one obtains smooth families of Fano surfaces and intermediate Jacobians
of these threefolds. This is a joint work in progress with Evgeny Shinder. | 
