Posted on 12th April 2019

I spent much of the last week at the British Mathematics Colloquium on the sunny campus of Lancaster university. These are some notes to myself about interesting things I saw. The one downside to Lancaster hosting the event was their use of their (I guess central IT) fancy seminar announcement system. This means titles and abstracts have disappeared from the internet, and I have to work from my incomplete notes and memory.

Alice Guionnet kicked things off with a talk about random matrices. I was fascinated by some pictures of random tilings with triangles; here are some internet links:

- Random lozenge tilings. Follow the links for lots of great pictures. Paper here: arXiv:1310.5844 [math.PR]
- Pictures from Vadim Gorin.

Then followed some "speed talks" by Phd Students: literally 5-10 minutes to present a talk. This was done remarkably well by all concerned. In particular, I liked the talk by Wirzenius on this paper: arXiv:1811.09402 [math.FA] Another talk was about percolation, focusing on Diffusion-limited aggregation which was new to me.

Janos Pach finished off the day with a fun, easy to understand (but one suspects the proofs are rather deep) talk about graph theory.

I was late to arrive Tuesday, but listed to an interesting algebra talk by Michel Broue, and then a talk by Charlie Stripp of the MEI on the Mathematics A-Level reform. The afternoon was Analysis talks, on harmonic analysis, a lovely talk by Mike Whittaker on monotilings, coarse geometry, and a talk on non-commutative Fourier transforms (which I wonder has links to my work on non-commutative \( L^p \) spaces). Sadly I had to head home, and so missed the public lecture.

After teaching on Wednesday morning (and so missing Monod's talk) I arrived for the Analysis session. Three great talks, on von Neumann algebras, semigroups of operators, and semigroup \( C^* \)-algebras. There was then an LMS meeting, and a talk by Kathryn Hess; her talk was similar to this one (youtube).

On Thursday I saw Piotr Koszmider give a survey talk on \( C(K) \) spaces and indecomposibility, and related ideas (and it was all the better for being survey like!) The Gil Kalai finished off the conference with a broad-side against quantum computers.

There then followed a meeting of NBFAS of which I attended just the Thursday part. Lyudmilla Turowska spoke about Operator Synthesis, which I have long been interested in. A new innovation was then to have some shorter "workshop" talks, but postdocs. Sam Evington gave a lovely white-board talk about some recent work in \( C^* \)-classification, and Lefteris Kastis spoke about non-selfadjoint algebras.

Some ideas which came up in conversations:

- Odometer actions, and the Bunce Deddens algebra
- Schreier graphs and links to
- Self-similar groups.

I haven't been a general mathematics meeting in many, many years, and haven't been to NBFAS for a while. I was glad I attended both: the quality of talks seemed to be excellent (perhaps age, and associated greater understanding of at least the surface of lots of different subjects, helps with getting *something* out of any talk) and I continue to be impressed by people who are brave enough to give a white-board talk under time pressure.