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Abstracts


Oscar Randal-Williams (Cambridge):
Metastable cohomology of moduli spaces of Riemann surfaces

A central object of interest in the study of moduli spaces of Riemann surfaces is their cohomology, which describes invariants - characteristic classes - for families of Riemann surfaces. In 1985 Harer proved the remarkable theorem that the cohomology of the moduli space of genus g surfaces is independent of the genus in a range of degrees tending to infinity with g: Madsen and Weiss' 2007 proof of the Mumford Conjecture completely described the cohomology in this stable range.
I will describe joint work with S. Galatius and A. Kupers in which we show there is a larger range of degrees, the metastable range, in which the cohomology is no longer stable but becomes periodic in a certain sense. The main technical tool is a theory of cellular E_2-algebras, which I shall explain in some detail my first talk. In my second talk I will describe how this general theory applies to moduli spaces of Riemann surfaces.


Daniel Luckhardt (Augsburg):
Benjamini-Schramm convergence of normalized characteristic numbers

On a class of closed oriented Riemannian manifolds with lower bounds on curvature and injectivity radius we study the parameter given by a characteristic number over the volume of the manifold. The domain of this parameter is endowed with the Benjamini-Schramm (BS) topology, a weak version of pointed Gromov-Hausdorff convergence. Using Chern-Weil theory, one can show that this parameter is continuous and has a continuous extension to the completion of its domain in the BS topology. From the known fact that this completion is compact one can derive a testability result for characteristic numbers as well as a uniform bound on any fixed characteristic number in terms of the volume.


Gerrit Herrmann (Regensburg):
Thurston norm and L^2-Betti numbers

In my talk I will define the Thurston norm of a closed irreducible 3-manifold M. This is a semi-norm on the second homology H_2(M;Z). Morally speaking it measures the complexity of a class by embedded surfaces representing this class. I will then characterize embeddings of surfaces which release the Thurston norm by certain L^2-Betti numbers.


Clara Löh (Regensburg):
Twisted simplicial volumes

Simplicial volumes measure the complexity of manifolds in terms of weighted numbers of singular simplices. The case of real coefficients corresponds to classical simplicial volume and has interesting connections with geometry. Other choices of (twisted) coefficients are tailored to more combinatorial, ergodic theoretic or large-scale aspects. This talk surveys different choices of coefficients and their use cases.


Manuel Amann (Augsburg):
Orbifolds with all geodesics closed

The concept of a Riemannian orbifold generalises the one of a Riemannian manifold by permitting certain singularities. In particular, one is able to speak about several concepts known from classical Riemannian geometry including geodesics. Whenever all geodesics can be extended for infinite time and are all periodic, the orbifold is called a Besse orbifold —in analogy to Besse manifolds. A classical result in the simply-connected manifold case states that in odd dimensions only spheres may arise as examples of Besse manifolds.
In this talk we shall illustrate that the same holds for Besse orbifolds, namely that they are actually already manifolds whence they are spheres. The talk is based on joint work in progress with Christian Lange and Marco Radeschi.


Stefan Schreieder (München):
Kaehler structures on spin 6-manifolds

We use the minimal model program to study the topology of spin 6-manifolds that carry a Kaehler structure. We show that many spin 6-manifolds have the homotopy type but not the homeomorphism type of a Kaehler manifold. Moreover, for given Betti numbers, there are only finitely many deformation types and hence topological types of smooth complex projective spin threefolds of general type. This talk is based on joint work with L. Tasin.


Justin Noel (Regensburg):
Blue-shift and thick tensor ideals

I will discuss a recent generalization of Kuhn's Blue-shift theorem about Tate cohomology. Combining this result with work of Arone, Dwyer, and Lesh we resolve a conjecture of Balmer and Sanders and classify the thick tensor ideals of compact genuine $A$-spectra, where $A$ is a finite abelian group. This is joint work with Tobias Barthel, Markus Hausmann, Niko Naumann, Thomas Nikolaus, and Nathaniel Stapleton.