David Harbater (University of Pennsylvania)
The Oort conjecture states that every cyclic branched cover of curves in characteristic p can be lifted to such a cover in characteristic zero. This raises the more general question of which finite groups G have the property that every G-Galois branched cover of curves in characteristic p can be lifted to characteristic zero. While this can be viewed as analogous to the inverse Galois problem, the situation here turns out to be very different, and the finite groups that have the lifting property are quite constrained. This talk will discuss the Oort conjecture and its generalizations, presenting in particular recent developments.