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 ( a (dot) guidolin (at) soton.ac.uk ) if you have questions.
More Pure Maths talks at Southampton: we run Pure Maths Colloquia, Topology Seminar, and Pure Postgraduate Seminar (link soon).
I will define roughly median spaces, they include hyperbolic spaces, trees and products of those. I will discuss group actions on roughly median spaces and the conjecture that proper actions on Lp spaces should be equivalent to proper actions on roughly median spaces.
The classical Alexander trick implies that the space of homeomorphisms of a d-dimensional disk is contractible. Recent work of Galatius-Randal-Williams and Krannich-Kupers extends this result to contractible manifolds of dimension at least 5. We aim to give a survey of the classical approach to studying automorphisms of manifolds in a modern language, and outline why these techniques currently fail to establish an analogous result in dimension 4. If time permits, we may briefly discuss the approach chosen by the authors named above, and discuss the obstacles to extending it to dimension 4.
When the characteristic of a field k divides the order of a finite group G, representation theory becomes more subtle. In this modular setting, Maschke's theorem fails, and not all kG-modules are semi-simple or even projective. The Green correspondence offers a powerful tool: under certain conditions, it gives a bijection between the non-projective indecomposable modules of G and those of a subgroup. In this talk, we'll explore how this correspondence plays out in a concrete case: the group SL_2(F_p) over an algebraic closure of F_p. We'll discuss what the Green correspondence tells us, the challenges in making it explicit, and what this reveals about modular representation theory in practice.
I will discuss the question of whether there can be an algorithm to decide contractibility of (usually finite) simplicial complexes, where there are many known results and some famous open problems.