Termine

Abstract: The Higman-Thompson groups consist of certain piecewise linear automorphisms of intervals. Szymik and Wahl prove homological stability for this family of groups, and compute the stable homology to be that of the infinite loop space of the Moore spectrum. We give a new proof of this result using scanning methods on a topological model for the disjoint union of these groups, using Thumann's framework of operad groups.

Markus Stroppel will give a lecture series on advanced topics in locally compact groups. The lectures take place on Monday at 14:15 in room SR 1D They will start on Monday, November 17. The planned topics are: * the scale function and tidy subgroups * automorphism groups of trees

I will report on a joint work in progress with Andreas Kollross, in which we are extending the classification of isometric cohomogeneity-one actions on irreducible symmetric spaces of compact type obtained by Kollross in 1998 to the general reducible case. In order to do so, we first obtain an explicit classification of isometric transitive actions on the aforementioned (reducible) spaces up to subgroup-conjugacy by using the works of Onishchik on decompositions of simple compact Lie algebras. I will restrict to the (less convoluted) case when all the de Rham factors are of non-group type and make comments on the general case.

An important question in integral p-adic Hodge theory is the study of lattices in crystalline Galois representations. There have been various classifications of such objects, such as Fontaine?Lafaille?s theory, Breuil?s theory of strongly divisible lattices, and Kisin?s theory of Breuil?Kisin modules. Using their prismatic theory, Bhatt?Scholze give a site-theoretic description of such lattices, which has the nice feature that it can specialize to many of the previous classifications by ?evaluating? suitably. In this talk, we will recall their result and explain an extension to the Lubin?Tate context.

For a topological group G, let Aut(G) be the group of all automorphisms, and let w(G) be the number of orbits of Aut(G) on G. I will report about results characterizing classes of groups G with suitable (topological or algebraic) assumptions on G, combined with bounds on w(G). In particular, there are strong results in the following cases: * G is locally compact and connected, with w(G) less than the cardinality of the continuum * G is compact, and w(G) is finite * G is finite, and w(G) < 5

I'll give an overview of stable rank one and the C*-algebras known to have it, then describe a new approach to studying stable rank one in possibly nonnuclear crossed products. As an application, we show that stable rank one is generic for two natural classes of minimal actions of free groups on the Cantor set. Time permitting, I will discuss some examples to motivate parts of the proof. This is joint work with Shirly Geffen and David Kerr.