EVENT DETAILS AND ABSTRACT

Title: A study of derived self-intersections
Speaker: Andrei Caldararu
Speaker Info: Wisconsin
Brief Description:
Special Note:
Abstract:

If X is a smooth subvariety of a smooth variety Y we study the derived intersection LX of X with itself inside Y. The resulting space is an algebro-geometric analogue of the space of paths in Y beginning and ending in X. As such it has a natural structure of homotopy groupoid. In my talk I shall discuss recent results with Arinkin which give a precise criterion for determining when LX is a linear fibration over X. If time will allow I'll also present results with Calaque and Tu on the more general question of determining when the homotopy groupoid LX is actually a dg-group scheme over X. The remarkable aspect of the entire story is the existence of a strong analogy between the algebro-geometric picture and problems in Lie theory and homotopy theory.