Mathematics Colloquium
This term the talks are aimed at a general mathematics audience. The main purpose of the talks is to bring the mathematics community at Royal Holloway together after a period of online talks. Visitors are very welcome!
SCHEDULE FOR AUTUMN 2021
13th October: Stefanie Gerke
Title: Second best structures in randomly weighted graphs
Abstract: In this talk we give a brief introduction to randomly weighted graphs and then look at successive shortest paths. This will involve analysing Dijkstra's algorithm carefully for these graphs.
27th October: José Burillo (Polytechnic University of Catalonia)
Title: The Banach-Tarski paradox and amenability
Abstract: As is well-known, the Banach-Tarski paradox states that a ball can be split in a finite number of sets, which rearranged, produce two balls of the same size as the original. (alternatively, a ball of different size, also known as the pea-and-the-sun paradox). We will show an elementary proof of this fact, and discuss the group theory related to it. A concept which is pivotal in understanding the paradox is amenability, a property of the groups of isometries which detects this behaviour. We will give an overview of this concept and its implications for the paradox.
10th November: Simon Blackburn
Title: Non-overlapping codes
Abstract: A code C is a set of q-ary words of length n. The code C is non-overlapping if the end of one element x in C is never equal to the start of another element y in C. (Here we include the case when x and y are the same word.) For given values of q and n, how large can C be?
