Participants of HCM Workshop: Automorphisms of Manifolds (click to enlarge)

# HCM Workshop: Automorphisms of Manifolds

Date: September 2 - 6, 2019

Venue: Lipschitz lecture hall, Mathematics Center, Endenicher Allee 60, 53115 Bonn,

Organizers:

• Fabian Hebestreit (University of Bonn)
• Wolfgang Lück (University of Bonn)

The workshop is financed by the ERC Advanced Grant KL2MG-interactions'' (no.662400) of Wolfgang Lück granted by the European Research Council.

Click here for the schedule (inactive)

## Abstract

The aim of the workshop is to bring together a small group of researchers to study the recent developments in the analysis of homotopy types of diffeomorphism groups. Following the work of Michael Weiss on the Pontryagin classes of euclidean fibre bundles and the proof of higher dimensional analogues of Mumford's conjecture by Galatius and Randal-Williams (following the solution of the latter by Madsen-Weiss), there has been a flurry of work exploiting ideas introduced by these authors.

On the one hand Alexander Kupers and Oscar Randal-Williams made progress in understanding the rational homotopy groups of spaces of diffeomorphisms of discs by exploiting a fibre sequence introduced by Michael Weiss, which connects these groups to the embedding tower of certain highly connected manifolds and their diffeomorphism groups.
On the other hand Thomas Willwacher produced a rational graph-complex model for the embedding tower in equal dimension, that, while not known to converge to the diffeomorphism group, suggests a new approach and in particular produces many new candidate classes to be analysed. This compares to computations of Alexander Berglund, who used the traditional surgery-and-K-theory method to produce a rational model for the diffeomorphism group of simply connected manifolds in the concordance stable range, that shows Willwacher's predictions might be closer to the truth than anticipated. Finally, very recent work of Tadayuki Watanabe shows that many of Maxim Kontsevich's proposed characteristic classes are non-trivial on the 4-disc by yet another application of graph complexes.

The main goal of the workshop is to have these authors explain their work in detail, so as to gain insight into the parallels and differences between the approaches and hopefully play them off against each other fruitfully.

# List of Speakers

• Alexander Berglund (Stockholm)
• Alexander Kupers (Harvard)
• Oscar Randal-Williams (Cambridge)
• Tadayuki Watanabe (Shimane)
• Thomas Willwacher (ETH Zuerich)
• Michael Weiss (Münster)

Participation will only be possible by invitation!