Mon, 02 Jun 2025
16:00
L6

On the largest $k$-product-free subsets of the Alternating Groups

Anubhab Ghosal
(University of Oxford)
Abstract

A subset $A$ of $A_n$ is $k$-product-free if for all $a_1,a_2,\dots,a_k\in A$, $a_1a_2\dots a_k$ $\notin A$.
We determine the largest $3$-product-free and $4$-product-free subsets of $A_n$ for sufficiently large $n$. We also obtain strong stability results and results on multiple sets with forbidden cross products. The principal technical ingredient in our approach is the theory of hypercontractivity in $S_n$. Joint work with Peter Keevash.

Mon, 26 May 2025
16:00
L6

Large values of Dirichlet polynomials with characters

Vishal Gupta
(University of Oxford)
Abstract

Dirichlet polynomials are useful in the study of the Riemann zeta function & Dirichlet L functions, serving as approximations to them via the approximate functional equation. Understanding how often they can be large gives bounds on the number of zeroes of these functions in vertical strips - known as zero density estimates - which are relevant to the distribution of primes in short intervals. Based on Guth-Maynard, we study large values of Dirichlet polynomials with characters, relevant to Dirichlet L functions. Joint work with Yung Chi Li. 

Mon, 19 May 2025
16:00
L6

On derived deformations of Galois representations (after Galatius-Venkatesh)

Samuel Moore
(University of Oxford)
Abstract


Given a mod $p$ Galois representation, one often wonders whether it arises by reducing a $p$-adic one, and whether these lifts are suitably 'well-behaved'. In this talk, we discuss how ideas from homotopy theory aid the study of Galois deformations, reviewing work of Galatius-Venkatesh.

Mon, 12 May 2025
16:00
L6

The moduli space of Bohr sets in R^n

Yaël Dillies
(Stockholm University)
Abstract

The arithmetic regularity lemma says that any dense set A in F_p^n can be cut along cosets of some small codimension subspace H <= F_p^n such that on almost all cosets of H, A is either random or structured (in a precise quantitative manner). A standard example shows that one cannot hope to improve "almost all" to "all", nor to have a good quantitative dependency between the constants involved. Adding a further combinatorial assumption on A to the arithmetic regularity lemma makes its conclusion so strong that one can essentially classify such sets A. In this talk, I will use use the analogous problem with F_p^n replaced with R^n as a way the motivate the funny title.

Multivariable Vandermonde determinants, amalgams of matrices and Specht modules
Brown, F Journal of Algebra (01 Apr 2025)
Pattern formation along signaling gradients driven by active droplet behaviour of cell groups
Ford, H Celora, G Westbrook, E Dalwadi, M Walker, B Baumann, H Weijer, C Pearce, P Chubb, J Proceedings of the National Academy of Sciences volume 122 issue 21 (23 Apr 2025)
A note on indefinite matrix splitting and preconditioning
Wathen, A Linear Algebra and its Applications (23 Apr 2025)

The old mathematical ones are the best. Surprisingly popular on social media given you might actually need some maths to get it. Actually, not surprising at all.

Here's Vishal.

A one-mile road run open to the general public celebrating Roger Bannister’s historic achievement of breaking the mile world record in Oxford on May 6th, 1954.

Open to participants of all ages and abilities. Enter as an individual or as a team (including departmental teams).

Full info for the 5th May event

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