University of Bristol, Wednesday February 7th 2018
Venue: Lecture theatre SM1, School of Mathematics, University of Bristol
Owing to exceptional budget constraints we politely request that any postgraduate who will be requesting that we cover their travel expenses seek-out the cheapest means of getting here possible (typically a pre-booked train is fine – note that most people in this category are elgibile for a rail-card).
Let p be any prime and n be any natural number. Let χ be an ordinary irreducible character of the symmetric group Sn whose degree is coprime to p.
We bound the number of p’-irreducible constituents of the restriction of χ to Sn−1. This generalizes work of Ayyer, Prasad and Spallone (2016) for the prime p = 2. This is joint work with E. Giannelli and S. Martin.
Some years ago, Lachlan advanced a theory on homogeneity in relational structures which imposed a natural “hierarchy of complexity” on the universe of homogeneous relational structure. This theory was reworked by Cherlin in the 1990’s with a view to understanding finite permutation groups from a model theoretic point of view.
One upshot of all this is that we know the existence of an infinite family of theorems describing the so-called “relational complexity” of all finite permutation groups. The problem is that, although we know these theorems exist, and even have a “form” for them, nonetheless we do not yet have the precise statement of any of them. However Cherlin has conjectured what (part of) the first of these theorems should say, and we will discuss this conjecture at some length.
There has also been substantial progress on this conjecture due to Cherlin himself, to Wiscons, and to myself and various co-authors. In particular the recent results that I will describe are due to myself, Pablo Spiga, Francis Hunt and Francesca Dalla Volta.
The talk has elements of model theory, combinatorics and finite permutation groups, and should be accessible to all.