Title: Differential topology in infinite dimensions
Abstract: Infinite dimensional manifolds play an important role in the study of non-linear PDE's. When studying the topology of these spaces we encounter several interesting phenomena. For example, unlike the finite dimensional case, the infinite dimensional sphere and general linear group are contractible. In this talk, I will discuss ongoing work together with Alberto Abbondandolo, Michael Jung, and Thomas Rot, extending classical ideas from differential topology to the infinite dimensional setting.