Derived and L-equivalence of manifolds in examples.

I will present several examples of derived and L-equivalent pairs of non-birational Calabi-Yau type manifolds aiming at understanding the relation between these two notions of equivalence. We will try to find a common geometric framework governing these examples. The talk will include joint work with Marco Rampazzo and with Grzegorz Kapustka and Riccardo Moschetti.