03/04/2017, 14:30 — 15:30 — Sala P3.10, Pavilhão de Matemática
Ricardo Campos, ETH Zurich
Configuration spaces of points and their homotopy type
Given a manifold $M$, one can study the configuration space of $n$ points on the manifold, which is the subspace of $M^n$ in which two points cannot be in the same position. The study of these spaces from a homotopical perspective is of interest in very distinct areas such as algebraic topology or quantum field theory. However, even if we started with a simple manifold $M$, despite the apparent simplicity such configuration spaces are remarkably complicated; even the homology of these spaces is reasonably unknown, let alone their (rational/real) homotopy type.
In this talk, I will give an introduction to the problem of understanding configuration spaces and present a combinatorial/algebraic model of these spaces using graph complexes. I will explain how these models allow us to answer fundamental questions about the dependence on the homotopy type of $M$. I will explain how these models give us new tools to address other problems such as understanding embedding spaces or computing factorization homology.
This is joint work with Thomas Willwacher based on arXiv:1604.02043.
