Title: Derived jet and arc spaces

Abstract: There has been significant and powerful advances in understanding the Kaehler differentials of jet and arc spaces, whose formula helps determine when properties of maps of schemes lift to properties of maps of local rings of arc spaces, so called arc ascent. The subject of the talk will be work in progress, joint with Roi Docampo and C. Eric Overton-Walker, which aims to generalize these formulae to the cotangent complex. To do this, we utilize animated rings (or derived algebraic geometry). The talk will be self-contained and all notions introduced and motivated. Time permitting, we will speculate on the homology of a certain complex as it relates to deformations of the arc space.