Termine

Abstract: The cohomology ring of moduli spaces of manifolds is an important object in geometric topology, as it classifies characteristic classes of manifold bundles. For even-dimensional manifolds, Galatius and Randal-Williams established a complete homotopy theoretic formula for this object after a certain stabilization procedure. In this talk, I will explain an odd-dimensional analog of Galatius and Randal-Williams' work in the context of odd-dimensional manifold triads. After stating this result, I will explain the strategy of proof and discuss some applications and examples.

In the previous talk, Fontaine equivalence was found to be a central tool for p-adic local Langlands correspondance for GL2(Qp). It describes the involved category of Galois representations in terms of another semilinear algebra category called étale (?,?)-modules. We will first explain why the case of GL2(K) bends towards the apparition of what may be called plectic (?,?)-modules using the work of Breuil-Herzig-Hu-Morra-Schraen. Then, we aim to give an overview of a Fontaine equivalence in this situation, as obtained in my thesis.

Pureness is a regularity property that plays a prominent role in the structure of C*-algebras. It can be thought of the $\mathcal{Z}$-stability at the level of the Cuntz semigroup of the algebra and at the same time is proved to be equivalent to certain weak comparison and divisibility properties. This characterization implies that every simple, non-elementary C*-algebra with a unique quasitrace and mild comparison has strict comparison. The characterization is also used to show that the class of pure C*-algebras behaves well under extensions. Further, for a separable C*-algebra $A$, one has that $\mathcal{Z}$-stability is equivalent to demanding that the uncorrected central sequence algebra of $A$ is pure, which in turn is equivalent to saying that said algebra is almost divisible. This is joint work with Ramon Antoine, Hannes Thiel, and Eduard Vilalta; and with Hannes Thiel and Eduard Vilalta.

Kolloquium über Geschichte und Didaktik der Mathematik