Please join colleagues in the Department of Statistics for their annual Florence Nightingale Lecture which will be held today, Friday 22nd May at 3.30pm in the Large Lecture Theatre, Department of Statistics. Everyone is welcome.

Packing the largest trees in the tree packing conjecture
Janzer, B Montgomery, R Journal of the European Mathematical Society (15 May 2026)
Sums of three positive cubes
Maynard, J Journal of the London Mathematical Society volume 113 issue 5 (05 May 2026)
Lattice models for phases and transitions with non-invertible symmetries
Bhardwaj, L Bottini, L Schäfer-Nameki, S Tiwari, A SciPost Physics volume 20 issue 5 (13 May 2026)
The Mechanical Virtue of Random Fourier Features and Model Complexity
Cartea, Á Shi, Y (2025)
Tue, 09 Jun 2026

14:00 - 15:00
L5

Permutations with an invariant set of size k

Ben Green
((Mathematical Institute University of Oxford))
Abstract

Denote by p(k) the limit, as n tends to infinity, of the probability that a random permutation on n letters has some invariant set of size k. For example, p(1) = 1 - 1/e. I will discuss the asymptotic behaviour of p(k). Joint work with Mehtaab Sawhney.

On a Clique‐Building Game of Erdős
Malekshahian, A Spiro, S Journal of Graph Theory (14 May 2026)
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