The talks are all happening at University of Southampton (in person), on Highfield Campus (SO17 1BJ). For the building and the room, see the individual postings. Email the organiser ( d (dot) kasprowski (at) soton.ac.uk ) if you have questions.
More Pure Maths talks at Southampton: we run Pure Maths Colloquia, Pure Lunchtime Seminar, and Pure Postgraduate Seminar (link soon).
The quadratic 2-type is a collection of invariants which plays a big role in the homotopy classification of 4-manifolds. I will recall a result from my talk last year that, for manifolds with fundamental group ZxZ/p, there are at most p many different homotopy types with fixed quadratic 2-type. I will explain how this has been improved to a complete classification by including an additional Z/p-valued intersection form, and also generalized to semidirect products of Z and Z/p.
I will describe how the homotopy groups of spheres may be generated using suspensions, Whitehead products, and higher order operations, starting from the identity map, and the inclusion of wedge summands. This may be viewed as an unstable analogue of a theorem of Joel Cohen. This is joint work with David Blanc and Debasis Sen.
In this talk we will investigate pullback fibrations that arise when taken over connected sums. In particular, when the fibre is an odd-dimensional sphere, we will discuss some conditions under which the total space itself has the homotopy type of a connected sum with a gyration. This is joint work with Stephen Theriault.
I will discuss a construction of finitely generated torsion-free groups for which any action on any finite-dimensional CW-complex with finite Betti numbers has a global fixed point.
A G-kernel is a group homomorphism from a (discrete) group G to Out(A), the outer automorphism group of a C*-algebra A. There are cohomological obstructions to lifting such a G-kernel to a group action. In the setting of von Neumann algebras, G-kernels on the hyperfinite II_1-factor have been completely understood via deep results of Connes, Jones and Ocneanu. In the talk I will explain how G-kernels on C*-algebras and the lifting obstructions can be interpreted in terms of cohomology with coefficients in crossed modules. G-kernels, group actions and cocycle actions then give rise to induced maps on classifying spaces. For strongly self-absorbing C*-algebras these classifying spaces turn out to be infinite loop spaces creating a bridge to stable homotopy theory. This project is joint work with S. Giron Pacheco and M. Izumi.