# Abstracts - Moduli and Traces

**Michael J. Hopkins** (Harvard University)

*Topological methods in condensed matter physics*

I will describe recent work with Dan Freed applying Madsen-Tillman spectra to classification problems in condensed matter physics.

**Oscar Randal-Williams** (Cambridge University)

*E _{n}-cells and applications*

The classifying spaces of many interesting families of groups can be arranged to form algebras over the little n-cubes operad E

_{n}(mapping class groups of surfaces with one boundary, automorphism groups of free groups, general linear groups, unitary groups, ...). I will explain some ongoing work with S. Galatius and A. Kupers in which we use a theory of "E

_{n}cellular homology" to produce cellular models for such E

_{n}-algebras with constraints on the dimensions of the cells which arise. Such constraints give immediate information about the homology of these groups (stability, secondary stability, ...).

**Nathalie Wahl **(University of Copenhagen)

*The homology of the Higman-Thompson groups*

We explain how homological stability combined with a "Madsen-Weiss" theorem allows the computation of the homology of the Higman-Thompson groups.

This is joint work with Markus Szymik, with an additional "scanning" approach, which is joint with Søren Galatius.

**John Rognes** (University of Oslo)

*Cubical and cosimplicial descent*

Joint with Bjørn I. Dundas. We prove that algebraic K-theory, topological Hochschild homology and topological cyclic homology satisfy cubical and cosimplicial descent at connective structured ring spectra along 1-connected maps of such ring spectra.

**Michael Weiss** (Universität Münster)

*The diffeomorphism group of a smooth homotopy sphere*

It is hard to detect the exotic nature of an exotic n-sphere M in homotopical features of the diffeomorphism group Diff(M). The well known reason is that Diff(M) contains a big topological subgroup H which is identified with the group of diffeomorphisms rel boundary of the n-disk, with a small coset space Diff(M)/H which is invariably homotopy equivalent to O(n+1). Therefore it seems that our only chance to detect the exotic nature of M in homotopical features of Diff(M) is to see something in this extension. I want to report on PhD work of O Sommer and calculations due to myself and Sommer which show that there is something to see in the case where M is the 7-dimensional exotic sphere of Kervaire-Milnor fame which bounds a compact smooth framed 8-manifold of signature 8.