Termine

There will be 6 speakers, each will have 6 minutes for a blackboard talk and 2 minutes to answer questions from the audience. The line-up and titles are follows: 1. Thomas Nikolaus: The heart of cyclotomic spectra 2. Thomas Tony: Scalar curvature rigidity and higher index theory 3. Robin J. Sroka: On the homology of Temperley-Lieb algebras 4. Devarshi Mukherjee: Homological epimorphisms in geometric group theory 5. Phil Pützstück: Equivariant Picard Spectra 6. Arthur Bartels: Flow spaces

There exists a natural higher dimensional generalisation of 4-dimensional ALF gravitational instantons of type A_n: the toric hyperkaehler manifolds of Bielawski and Dancer (2000). There are also known many examples of complete hyperkaehler manifolds, where the asymptotic behaviour of the metric should be described as being QALF of dihedral type. These include various monopole moduli spaces, Hilbert schemes of points on complex ALF surfaces, and, conjecturally, Coulomb branches of N=4 supersymmetric quantum gauge theories. In my talk, I shall present an approach to construction and classification of complete QALF hyperkaehler manifolds of dihedral type. This is a joint work with Lorenzo Foscolo.

In operator algebra theory central sequences have long played a significant role in addressing problems in and around amenability, having been used both as a mechanism for producing various examples beyond the amenable horizon and as a point of leverage for teasing out the finer structure of amenable operator algebras themselves. One of the key themes on the von Neumann algebra side has been the McDuff property for II_1 factors, which asks for the existence of noncommuting central sequences and is equivalent, by a theorem of McDuff, to tensorial absorption of the unique hyperfinite II_1 factor. We will show that, for a topologically free minimal action of a countable amenable group on the Cantor set, the von Neumann algebra of the associated dynamical alternating group is McDuff. This yields the first examples of simple finitely generated nonamenable groups for which the von Neumann algebra is McDuff. This is joint work with Spyros Petrakos.

Given some large positive integer N, what is the largest possible size of a subset of {1,...,N} which does not contain a three-term arithmetic progression (i.e. without three distinct elements x,y,z satisfying x+z=2y)? Similarly, given a prime p and a large positive integer n, what is the largest possible size of a subset of the vector space F_p^n which does not contain a three-term arithmetic progression (i..e without three distinct vectors x,y,z satisfying x+z=2y)? These are long-standing problems in additive combinatorics. This talk will explain the known bounds for these problems, give an overview of some of the proof techniques, and discuss additional applications of these techniques to other additive combinatorics problems.

Arrival Talks by Sam Shepherd, Anna Cascioli, Lawrence Lo and Björn Gebhard