Fridays@4

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.

In this Fridays@4 event – for this week renamed Fridays@1 (with lunchtime pizza) – Torkel Loman from the Mathematics Institute and Alastair McCullough from the Department of Computer Science will present their talks.

Torkel Loman
The behaviours of noisy feedback loops and where (in parameter space) to find them

Alastair McCullough 
Tech, Coffee, and the Regulation of Truth: An Enterprise Barista's Story

Torkel's abstract

Mixed positive/negative feedback loops (networks where a single component both activates and deactivates its own productions) are common across biological systems, and also the subject of this talk. Here (inspired by systems for e.g. bacterial antibiotics resistance), we create a minimal mathematical model of such a feedback loop. Our model (a stochastic delay differential equation) depends on only 6, biologically interpretable, parameters. We describe 10 distinct behaviours that such feedback loops can produce, and map their occurrence across 6-dimensional parameter space.

Are you thinking of launching your own start-up or considering joining an early-stage company? Navigating the entrepreneurial landscape can be both exciting and challenging. Join Pete for an interactive exploration of the unwritten rules and hidden insights that can make or break a start-up journey.

Drawing from personal experience, Pete's talk will offer practical wisdom for aspiring founders and team members, revealing the challenges and opportunities of building a new business from the ground up.

Whether you're an aspiring entrepreneur, a potential start-up team member, or simply curious about innovative businesses, you'll gain valuable perspectives on the realities of creating something from scratch.

This isn't a traditional lecture – it will be a lively conversation that invites participants to learn, share, and reflect on the world of start-ups. Come prepared to challenge your assumptions and discover practical insights that aren't found in standard business guides.
 

Speaker: Professor Pete Grindrod

In the fast-paced world of trading, where exabytes of data and advanced mathematical models offer powerful insights, how do you harness these to anticipate market shifts and evolving prices? Numbers alone only tell part of the story. Beneath the surface lies the unpredictable force of human behaviour – the delicate balance of buyers and sellers shaping the market’s course. 

In this talk, we’ll uncover how these forces intertwine, revealing insights that not only harness data but challenge conventional thinking about the future of trading.

Speaker: Chris Horrobin (Head of European and US people development for Optiver)

Speaker bio

Chris Horrobin is Head of European and US people development for Optiver. Chris started his career trading US and German bond options, adding currency and European index options into the mix before moving to focus primarily on index options. Chris spent his first three years in Amsterdam before transferring to Sydney. 

During these years, Chris traded some of the biggest events of his career including Brexit and Trump (first time around) and before moving back to Europe led the positional team in his last year. Chris then moved out of trading and into our training team running our trading education space for four years, owning both the design and execution of our renowned internship and grad programs. 

The Education Team at Optiver is central to the Optiver culture and focus on growth – both of employees and the company. Chris has now extended his remit to cover the professional development of hires throughout the business.

North meets South is a tradition founded by and for early-career researchers. One speaker from the North of the Andrew Wiles Building and one speaker from the South each present an idea from their work in an accessible yet intriguing way. 

North Wing

Speaker: Paul-Hermann Balduf
Title: Statistics of Feynman integral
Abstract: In quantum field theory, one way to compute predictions for physical observables is perturbation theory, which means that the sought-after quantity is expressed as a formal power series in some coupling parameter. The coefficients of the power series are Feynman integrals, which are, in general, very complicated functions of the masses and momenta involved in the physical process. However, there is also a complementary difficulty: A higher orders, millions of distinct Feynman integrals contribute to the same series coefficient.

My talk concerns the statistical properties of Feynman integrals, specifically for phi^4 theory in 4 dimensions. I will demonstrate that the Feynman integrals under consideration follow a fairly regular distribution which is almost unchanged for higher orders in perturbation theory. The value of a given Feynman integral is correlated with many properties of the underlying Feynman graph, which can be used for efficient importance sampling of Feynman integrals. Based on 2305.13506 and 2403.16217.

South Wing

Speaker: Marc Suñé 
Title: Extreme mechanics of thin elastic objects
Abstract: Exceptionally hard --- or soft -- materials, materials that are active and response to different stimuli, elastic objects that undergo large deformations; the advances in the recent decades in robotics, 3D printing and, more broadly, in materials engineering, have created a new world of opportunities to test the (extreme) mechanics of solids. 

In this colloquium I will focus on the elastic instabilities of slender objects. In particular, I will discuss the transverse actuation of a stretched elastic sheet. This problem is a peculiar example of buckling under tension and it has a vast potential scope of applications, from understanding the mechanics of graphene and cell tissues, to the engineering of meta-materials.

There will be free pizza provided for all attendees directly after the event just outside L1, so please do come along!

North Wing
Speaker: Alexandru Pascadi 
Title: Points on modular hyperbolas and sums of Kloosterman sums
Abstract: Given a positive integer c, how many integer points (x, y) with xy = 1 (mod c) can we find in a small box? The dual of this problem concerns bounding certain exponential sums, which show up in methods from the spectral theory of automorphic forms. We'll explore how a simple combinatorial trick of Cilleruelo-Garaev leads to good bounds for these sums; following recent work of the speaker, this ultimately has consequences about multiple problems in analytic number theory (such as counting primes in arithmetic progressions to large moduli, and studying the greatest prime factors of quadratic polynomials).

South Wing
Speaker: Tim LaRock
Title: Encapsulation Structure and Dynamics in Hypergraphs
Abstract: Within the field of Network Science, hypergraphs are a powerful modelling framework used to represent systems where interactions may involve an arbitrary number of agents, rather than exactly two agents at a time as in traditional network models. As part of a recent push to understand the structure of these group interactions, in this talk we will explore the extent to which smaller hyperedges are subsets of larger hyperedges in real-world and synthetic hypergraphs, a property that we call encapsulation. Building on the concept of line graphs, we develop measures to quantify the relations existing between hyperedges of different sizes and, as a byproduct, the compatibility of the data with a simplicial complex representation–whose encapsulation would be maximum. Finally, we will turn to the impact of the observed structural patterns on diffusive dynamics, focusing on a variant of threshold models, called encapsulation dynamics, and demonstrate that non-random patterns can accelerate spreading through the system.

Speaker: Mattia Magnabosco (Newton Fellow, Maths)
Title: Synthetic Ricci curvature bounds in sub-Riemannian manifolds
Abstract: In Riemannian manifolds, a uniform bound on the Ricci curvature tensor allows to control the volume growth along the geodesic flow. Building upon this observation, Lott, Sturm and Villani introduced a synthetic notion of curvature-dimension bounds in the non-smooth setting of metric measure spaces. This condition, called CD(K,N), is formulated in terms of the optimal transport interpolation of measures and consists in a convexity property of the Rényi entropy functionals along Wasserstein geodesics. The CD(K,N) condition represents a lower Ricci curvature bound by K and an upper bound on the dimension by N, and it is coherent with the smooth setting, as in a Riemannian manifold it is equivalent to a lower bound on the Ricci curvature tensor. However, the same relation between curvature and CD(K,N) condition does not hold for sub-Riemannian (and sub-Finsler) manifolds. 

Speaker: Rebecca Lewis (Florence Nightingale Bicentenary Fellow, Stats)
Title: High-dimensional statistics
Abstract: Due to the increasing ease with which we collect and store information, modern data sets have grown in size. Whilst these datasets have the potential to yield new insights in a variety of areas, extracting useful information from them can be difficult. In this talk, we will discuss these challenges.

The goal of Post-Quantum Cryptography (PQC) is to design cryptosystems which are secure against classical and quantum adversaries. A topic of fundamental research for decades, the status of PQC drastically changed with the NIST PQC standardization process. Recently there have been AI attacks on some of the proposed systems to PQC. In this talk, we will give an overview of the progress of quantum computing and how it will affect the security landscape. 

Group-based cryptography is a relatively new family in post-quantum cryptography, with high potential. I will give a general survey of the status of post-quantum group-based cryptography and present some recent results.

In the second part of my talk, I speak about Post-quantum hash functions using special linear groups with implication to post-quantum blockchain technologies.

CANCELLED DUE TO ILLNESS

The response of the Greenland and Antarctic ice sheets to a changing climate is one of the largest sources of uncertainty in future sea level predictions.  The behaviour of the subglacial environment, where ice meets hard rock or soft sediment, is a key determinant in the flux of ice towards the ocean, and hence the loss of ice over time.  Predicting how ice sheets respond on a range of timescales brings together mathematical models of the elastic and viscous response of the ice, subglacial sediment and water and is a rich playground where the simplified models of the contact between ice, rock and ocean can shed light on very large scale questions.  In this talk we’ll see how these simplified models can make sense of a variety of field and laboratory data in order to understand the dynamical phenomena controlling the transient response of large ice sheets.