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

It is well-established that Patterson-Sullivan measures on the boundary of a hyperbolic space, along with the associated Bowen-Margulis-Sullivan measure, provide valuable insights into the action of a group of isometries on the space's boundary through analysis of the geodesic flow. Given that paths of a random walk on a hyperbolic groups lie close to the group's quasi-geodesics, it is natural to ask whether similar behaviour can also be seen in the flow along bi-infinite random walk paths. In this talk, I will give an insight into classical Patterson-Sullivan theory, and show how studying bi-infinite random walks on a discrete hyperbolic group $G$ leads to an analogue of the Patterson-Sullivan measure on $\partial^2G$. This talk is based on joint work with Mahan Mj and Chiranjib Mukherjee.

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