Seminar: Scanning and Stability — Scrutinizing topological moduli spaces

Manuel Krannich will give a talk on Scanning and Stability — Scrutinizing topological moduli spaces.

Abstract: A topological moduli space consists, loosely speaking, of points representing geometric objects of some fixed kind, often embedded in an ambient space. In some cases, the moduli space can be understood by strolling through the surrounding space with a magnifying glass—a process called scanning. This approach can be used to provide proofs of remarkable theorems like the solution of the Mumford conjecture about the moduli space of smooth complex algebraic curves by Madsen and Weiss, the determination of the homotopy type of the bordism category by Galatius, Madsen, Tillmann and Weiss, the relationship between the symmetric group and the sphere spectrum by Barratt, Priddy and Quillen and the stable calculation of the homology of automorphism groups of free groups by Galatius. In this talk, I will introduce the idea of scanning and provide a very rough outline of proof of the theorems mentioned above.

The lecture is part of the ALG/NCG/TOP Ph.D. students' seminar.