Seminar Autumn 2024

18th September: Jan-Christoph Schlage-Puchta (University of Rostock)

Title: Numerical computation of the Witten zeta function of symmetric groups and Fenchel's conjecture

2nd October at 3pm: Robert Johnson (Queen Mary, University of London)

Title: Correlation and Intersection: from Sets to Permutations via Orders

Starts at 3pm!

We will discuss two extremal topics on permutations.

The first is analogues of the Harris-Kleitman inequality for families of permutations. It turns out that there are two natural notions of what it means for a family of permutations to be an up-set (corresponding to the strong and weak Bruhat orders) and surprisingly the correlation that occurs in the two cases is quite different. The second is a new notion of intersection for permutations.

Through these two examples, we will see a framework for translating extremal set theory concepts into the realm of permutations which has the potential to yield many open questions.

This is joint work with Imre Leader and Eoin Long.

9th October: Heather Leitch (Royal Holloway, University of London)

Title: Introduction to Quantum Computing, Error Correction, and Quantum LDPC Codes

Although quantum computers have the potential to solve problems far beyond the reach of classical computers, they have one major drawback: they are highly susceptible to noise. Quantum error correction (QEC) is crucial to overcoming these challenges before we can build a fault-tolerant quantum computer. In this talk I will give an overview of the fundamental concepts of quantum computing and quantum error correction before introducing the main area of my work, quantum Low-Density Parity-Check (LDPC) codes. These error correction codes offer a promising low overhead approach to achieving fault-tolerant quantum computation.

16th October: Antony Hilton (University of Reading)

Title: The total chromatic number of a graph

23rd October: Will Cohen (University of Cambridge)

Title: Cohomology of Profinite Groups Acting on Profinite Trees

Given an abstract group G, a natural question to ask is what properties of G are visible in finite quotients. In particular, one may ask whether the cohomology of G can be read off in this way. We call a group cohomologically separable if this is possible in a "natural" way, i.e. if the map from a group to its profinite completion induces an isomorphism in cohomology. In this talk, I will introduce properly the concepts of cohomological separability and some of the main methods we have for proving separability of particular groups. I will then discuss how such methods can be adapted to less well behaved environments, and present recent joint work with Wykowski where we are able to prove exactly when Baumslag--Solitar groups are cohomologically separable.

30th October: Álvaro Gutiérrez Cáceres (University of Bristol)

6th November: Steve Lester (King's College London)

13th November: Olivea Reade (Open University)

20th November: Clare Munro (University of Cambridge)

11th December:  Julia Wolf (University of Cambridge)