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)

En-cells and applications

The classifying spaces of many interesting families of groups can be arranged to form algebras over the little n-cubes operad En (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 "En cellular homology" to produce cellular models for such En-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.

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