The movable cone of a Calabi--Yau threefold

We study how the movable cone Mov(Y)Mov(𝑌) of a Calabi--Yau threefold Y𝑌 changes under deformation. In particular, we show that Mov(Y)Mov(𝑌) is a fundamental domain for the action of a certain reflection group on Mov(Ygen)Mov(𝑌gen), where Ygen𝑌gen is a general deformation of Y𝑌. This generalizes results of P. Wilson on the Kähler cone of Y𝑌.
If time permits, I will explain how to generalize these results to log Calabi--Yau threefolds and applications to the Morrison cone conjecture.

Note:
Refreshments at 3:30PM.