Please join us for a fireside chat, hosted by OSE, between PQShield founder and visiting professor, Dr Ali El Kaafarani, and Sami Walter, associate at Oxford Sciences Enterprises (OSE). 

Dr Ali El Kaafarani is the founder and CEO of PQShield, a post-quantum cryptography (PQC) company empowering organisations, industries and nations with quantum-resistant cryptography that is modernising the vital security systems and components of the world's technology supply chain.  

In this chat, we’ll discuss Dr Ali El Kaafarani’s experience founding PQShield and lessons learned from spinning a company out from the Oxford ecosystem.

It’s a busy and stressful term for a lot of us so come and take a break and do some colouring and origami with us. Venting is very much encouraged.

We’ll have an open discussion about the ways in which Mathematics is very euro-centric and how we can act, as students and educators, to change this.

TBC

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.

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. 

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.

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.