Promotion lecture Professor in Mathematics

Intersection theory deals with intersections of geometric objects such as varieties or more generally cycles. Classically, the intersection of two algebraic varieties is a cycle determined up to so-called rational equivalence. In the nineties local intersection numbers were defined at any point algebraically and geometrically. In general, there is no fixed representive of the global intersection that represents the local intersection numbers at each point.

I will discuss an analytic approach where we introduce more general geometric objects and define global intersections that represent all the local intersection numbers. This is based on joint work with Mats Andersson, Dennis Eriksson, Håkan Samuelsson Kalm, and Alain Yger.