14:00
Hyperbolic intersection arrangements
Abstract
Consider a connected graph and choose a subset of its vertices. From this simple setup, Iyama and Wemyss define a collection of real hyperplanes known as an intersection arrangement, going on to classify all tilings of the affine plane that arise in this way. These "local" generalisations of Coxeter combinatorics also admit a nice wall-crossing structure via Dynkin involutions and longest Weyl elements. In this talk I give an analogous classification in the hyperbolic setting using the data of an "overextended" ADE diagram with three distinguished vertices. I then discuss ongoing work applying intersection arrangements to parametrise notions of stability conditions for preprojective algebras.
14:00
Probabilistic laws on groups
Abstract
Suppose a finite group satisfies the following property: If you take two random elements, then with probability bigger than 5/8 they commute. Then this group is commutative.
Starting from this well-known result, it is natural to ask: Do similar results hold for other laws (p-groups, nilpotent groups...)? Are there analogous results for infinite groups? Are there phenomena specific to the infinite setup?
We will survey known and new results in this area. New results are joint with Gideon Amir, Maria Gerasimova and Gady Kozma.
OxWEST (Oxford Women in Engineering, Science and Technology) is running a 'what actually is a PhD' evening and we need your help. We're looking for PhD students to come and speak to undergraduates about what doing a PhD actually entails and answer any questions they may have to help them answer the dreaded question of 'should I do a PhD?'
Come by to G & D's on St Aldate's on Friday 1st November (week 3) at 8-10pm.