A conjecture of Orlov states that the Rouquier dimension of the derived category of a smooth projective variety is equal to its dimension. We'll discuss the meaning of the conjecture and some things we know about it, and then explain the proof of a weakened version. This weakened version implies a fact predicted by Orlov's conjecture: If X, Y are smooth projective varieties and there is a fully faithful functor from the derived category of X to the derived category of Y, then the dimension of X is at most the dimension of Y. Speaker(s): Noah Olander (Columbia University)