CIRCA seminar 30th November

There will be a CIRCA seminar on November 30th, at 1pm on Theatre D of Maths. Peter Cameron and Richard Connor will speak.

Peter’s title is “When is the commuting graph split or threshold?”.

Abstract: The commuting graph of a group (or semigroup) G has vertex set G, two vertices joined if they commute. It was introduced by Brauer and Fowler in 1955, in their seminal work on involution centralisers in simple groups.
Split graphs and threshold graphs are two subgraph-closed graph families arising in operations research. A graph is split if the vertex set is the union of a complete graph and a null graph (with maybe some edges between); it is threshold if there are vertex weights and two vertices are joined if the sum of their weights exceeds a threshold.
I hope to present the complete proof of the classification of groups whose commuting graph is split or threshold: they are either abelian, or generalised dihedral of twice odd order.

Richard’s title is “Similarity search by graph navigation: some high-dimensional problems”

Abstract: Similarity search is a simple concept: to (efficiently) find, from within a (very) large collection, those objects which are most similar to a query object presented from the same domain. We (kind of) know that even approximate search becomes linear-time when the data is “high dimensional”, and linear time is no use to us! Unfortunately, “high” means something like over 20 Euclidean dimensions, and our main current interest is in searching embeddings, which are high-dimensional vectors arising from convolutional neural networks (such as GPT.) Language model embeddings have thousands of dimensions.

Some interesting recent systems have emerged which use novel graph navigation techniques. Simply, each element of the collection is represented as a graph node, and nodes are connected according to some relation. Search strategy is something like: start at a random node and navigate the graph, at each step moving closer to the query, which should thus be reached in a logarithmic number of steps. The current “state-of-the-art” is hnswlib (Hierarchical Navigable Small-World), which claims to work independently of dimensionality.

That, of course, isn’t true! In this talk, we examine the essential concepts presented by the authors, and some unfortunate properties of high-dimensional spaces which spoil the low-dimensional intuitions of graph navigation.

All welcome!

CIRCA seminar 16th November

There will be a CIRCA seminar on 16th November, at 1pm in Theatre D of Maths.

Mun See Chang will speak on “Enriching Transformations for Dependently Typed Languages”.

Ursula Martin will speak on “The Social Machine of Mathematics”

Ursula’s abstract is: How does mathematics come about? In this talk I’ll look at what philosophers, social scientists and historians can tell us about what we are doing when we do mathematics, including recent work on explanation in mathematics, and on how mathematics has impact. I’ll also highlight new approaches to collaborative mathematics, computer supported formal proof, and AI-assisted proof, which challenge our understanding of what a proof might be.

All welcome!

CIRCA seminar 2nd November

There will be a CIRCA seminar on November 2nd, at 1pm in Theatre D of Maths.

Edwin Brady will speak on “The Idris Programming Language”

Details: I will talk about the Idris Programming Language, a language which (like Lean) is based on dependent type theory and (unlike Lean :)) is developed primarily in St Andrews with help from researchers and developers around the world. It is intended for general purpose programming, and supports formal reasoning about those programs. I will give some introductory examples which show how programming and theorem proving interact, and show how we are using dependent type theory to help develop robust and verifiable software.

Jon Fraser will speak on “Fourier analysis in finite fields”.

Details: I will discuss various counting problems in vector spaces over finite fields and show how a ‘Fourier analytic’ approach can help.

All welcome!

CIRCA seminar 5th October

On 5th October at 1pm in Maths D, Peiran Wu will talk about Lean, the theorem prover. We’ll then discuss setting up a study group to put some group theory into Lean. All welcome.

First CIRCA seminar of the year

There will be a CIRCA seminar on Thursday 21st September at 1pm in Theatre D of Maths.

Ian Miguel will speak on Puzznic and Colva Roney-Dougal will count the subgroups of the symmetric group.

Ruth Hoffman wins EPSRC grant

Ruth has just been awarded £199211 by EPSRC for a grant called “Enhancing Group Search with Graph Techniques”. The grant will run from now until July 2025. Congratulations Ruth!

Visit of Arne Van Antwerpen

Arne Van Antwerpen will be here on 16/17/18 May, visiting Olexandr Konovalov.

Arne will give a CIRCA seminar on the Wednesday afternoon, 4-5 in Theatre C.

Title: Multipermutation solutions of the Yang-Baxter equation and nilpotency of skew braces

Abstract: This talk will be based on joint work with Eric Jespers and Leandro Vendramin. The class of multipermutation solutions is a particularly interesting class of solutions of the celebrated Yang-Baxter equation (coming from mathematical physics) with a beautiful combinatorial structure. It was shown that this class corresponds to right nilpotent skew left braces of nilpotent type. In this talk we delve deeper into this class of skew left braces and identify the class of centrally nilpotent skew braces. We discuss that these behave very similar to nilpotent groups and will identify several possible central series for these objects. If time permits, we use this class to illustrate several other key concepts of skew left braces. The talk will be rife with examples and exciting open problems.

All welcome!

Visit of Pascal Schweitzer

Pascal Schweitzer from TU-Darmstadt will visit CIRCA on Wednesday May 10th, and give a talk at 4pm in Maths C. All welcome.

CIRCA seminar

The final CIRCA seminar of the semester will be on 13th April, at 1pm in Theatre C of Maths.

Ian Gent will speak on A Dream Model for Black Hole

Murray Whyte will speak on Irredundant monoid presentations

All welcome

Remaining CIRCA seminars this term

The final two CIRCA seminars of term will be

Thursday 17th November: Finn Smith and Jacob Beaddie

Thursday 24th November: Michael Young and Peter Cameron. Note the unusual date for this one, and also that it will be in Purdie C rather than Maths.