Termine

By definition, a group is profinitely rigid if it is determined up to isomorphism by its finite quotients amongst all finitely generated residually finite groups. In this talk I will present some results on the question of profinite rigidity of Coxeter groups. I will also explain how profinite rigidity of Coxeter groups is connected to the isomorphism problem of these groups.

The goal of this talk is to introduce the notion of lax idempotent monads, or more generally, lax idempotent algebras, in the context of homotopy-coherent mathematics. After reviewing the main definitions and properties, I will give examples of lax idempotent monads appearing in the theory of fibrations of (?,1)-categories, (co)completions, and (?,1)-operads. This is joint work with Thomas Blom.

Abstract: The metric completeness, geodesic completeness, and geodesic convexity of shape spaces, such as diffeomorphism groups, spaces of immersed curves, and spaces of immersed surfaces, have been studied intensively over the last twenty years. As in finite dimensions, geodesic completeness is a natural starting point for studying the existence of periodic geodesics. In infinite dimensions, however, the existence of periodic geodesics remains largely open, apart from a few special cases. We present existence results for periodic geodesics on half-Lie groups equipped with strong right-invariant Riemannian metrics under suitable regularity and completeness assumptions. Examples include Sobolev diffeomorphism groups. We also discuss analogous results for more general strong Riemannian Hilbert manifolds, where additional compactness assumptions, such as Palais--Smale type conditions, are required. This is joint work in progress with Martin Bauer.

I will speak on the classification problem of compact homogeneous Einstein spaces G/H. Recall that a G-invariant Einstein metric can be characterized as a critical point of the scalar curvature function restricted to the space of G-invariant metrics of volume one. To this end, I will introduce a new simplicial complex (defined by certain intermediate subgroups H

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Introduced by Ozawa, W*-bundles can be understood as continuous fields of tracial von Neumann algebras over a compact Hausdorff space. To study W*-bundles, we thus need to analyze von Neumann algebraic phenomena in a way that varies continuously. This work proves several C*-algebraic regularity properties, such as real rank zero, stable rank one, and comparison of projections for a class of W*-bundles that includes all locally trivial II_1-factor bundles. Namely, we consider W*-bundles which are selfless, or which admit a sequence of asymptotically free Haar unitaries, where the freeness occurs with respect to the trace in each fiber, uniformly over all fibers of the bundle. The proofs use Baire-category arguments where the density of each open set is demonstrated using perturbations by an approximately free element. For instance, to prove stable rank, or density of invertible elements, we consider perturbing a given x by a free circular operator, which will regularize it to something with trivial kernel, which we show admits a polar decomposition in the bundle. This is based on joint work, to appear soon, with Stuart White and Maxwell Ryder