05. Juli 2023
Thomas Rot (Vrije Universiteit Amsterdam)
From the infinite to the finite
Many elliptic PDE problems can be solved as zero finding problems of non-linear proper Fredholm mappings f:H\rightarrow H, where H is an infinite dimensional Hilbert space. We want to understand these mappings up to homotopy (i.e. perturbations) and understand their zero sets. In this talk I will give a full classification in terms of a well-studied, but complicated, object in algebraic topology: the stable homotopy groups of spheres. I will try to keep the neccessary topological background minimal. This is joint work with Lauran Toussaint.