Abstract TBA
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).
Abstract TBA
Abstract TBA
In 1966 Jane Matthews claimed that the conjugacy problem is solvable in the standard restricted wreath product A \wr B if and only if (i) the conjugacy problem is solvable in A and B and (ii) B has a solvable power problem. We will discuss this result, showing that an additional condition is required - that either A is abelian or B has a solvable order problem. We will also seek to extend this result to the permutational restricted wreath product A \wr_S B where, rather than acting on itself, B acts on a set S.
For an infinite graph, a periodic colouring of the vertices is one that is invariant under a subset of the symmetries of the graph. As such, a natural consideration are those locally finite quasi-transitive graphs with finite quotient. Recent work from Abrishami and collaborators investigates whether all such graphs permit proper periodic colourings, with conclusions dependent on the number of ends. An observation of Hopf tells us any infinite locally finite, quasi-transitive graph has 1, 2, or ∞-many ends. One case was left uncertain; do all locally finite quasi-transitive planar graphs with 1-end permit a periodic colouring? In this talk I will review the results of Abrishami and collaborators before describing how, through a theorem of Babai providing embeddings of 3-connected graphs into the Euclidean or hyperbolic planes, we can leverage properties of isometry groups to complete this investigation.
This talk connects ideas from geometric group theory, stochastic processes, and machine learning. We present a subtle Lipschitz result showing that for a norm-preserving group action, a bound on the generating set induces a bound on distances between points within an orbit. We begin with graph symmetry as a motivating example: the action of the permutation group on vertices. We then prove our main result in the context of the general theory of stochastic orbit processes. Finally, we explore connections to equivariance in machine learning.