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The Mathematical Finance Group in Oxford has long been a leader in research on financial mathematics. In recent years a number of research areas have become key focal points within the Group, notably behavioural finance and financial big data, robust pricing and machine learning. In particular, research has focused on financial stability, an area that became critical after the Financial Crisis in 2008. 

Prof. Doyne Farmer and some of his students are working on modelling complex financial systems and the ways that losses and financial distress can spread through such systems. In particular, the Group is looking at how to design a model that accurately captures the losses the banking system, shadow banking system and real economy could incur in another crisis. These models are called 'stress tests' and are nowadays conducted by most major banks. However, the current methodology of the stress tests does not capture the network of interbank connections, although this has been the major driver of losses in a crisis. Prof. Doyne Farmer's group is developing models that more accurately capture these interconnections. 

Today, a letter published in the Financial Times, discusses exactly this: the methodology of existing stress tests and their limitations.

When one wants to describe the symmetries of any object or system, in mathematics or everyday life, the right language to use is group theory. How might one go about understanding the universe of all groups and what kinds of novel geometry might emerge as we explore this universe?

The understanding of the possible geometries in dimension 3 is one of the triumphs of 20th century mathematics. In his Chairman's Inaugural Public Lecture, Professor Martin Bridson explains this triumph and why such an understanding is impossible in higher dimensions.

When you think about the founders of computing you may think Alan Turing, you may even think Charles Babbage. But you should definitely think about Ada Lovelace. Ada Lovelace is not only the link between Babbage and Turing, but a woman of fierce originality and intellectual interests whose ideas went beyond Babbage’s ideas of computers as manipulating numbers, and focused on their creative possibilities and their limits, the very issues with which we are wrestling today.

On 9 and 10 December the University of Oxford's celebrations of the 200th anniversary of Ada’s birth will culminate in a two-day Symposium exploring Ada's life and work, the scientific and cultural world around her and her continuing influence on science and the arts today. This Symposium will be streamed live.

Humans love to find an explanation that fits the facts, and fits them as closely as possible. But this often turns out to be a terrible way of learning about the world around us.

In the latest instalment of the Oxford Mathematics Alphabet we look at Bayes’ Theorem and how it is used in criminology, product recommendations, artificial intelligence, and recently in the search for the missing Malaysian Airliner MH370.

Tweedledum: "I know what you’re thinking about, but it isn’t so, nohow."
Tweedledee: "Contrariwise, if it was so, it might be; and if it were so, it would be: but as it isn’t, it ain’t. That’s logic."

If Charles Dodgson (Lewis Carroll) had not written Alice’s Adventures in Wonderland and Through the Looking-Glass, he’d probably be remembered as a pioneer photographer. But his Oxford ‘day job’ was as Lecturer in Mathematics at Christ Church. What mathematics did he do?  Find out in the latest in our poster series of Oxford Mathematicians.

 Lewis Carroll.pdf

A booklet about networks literacy developed by Mason Porter, Fellow of Somerville College and Professor of Nonlinear and Complex Systems in the University of Oxford's Mathematical Institute, in collaboration with colleagues from the USA, could help people understand all types of networks from social media to rabbit warrens. Mason was part of a team of over 30 network-science researchers, educators, teachers, and students who have written the booklet on networks literacy that schools can adapt to teach students the core concepts about networks.

"The concept of networks is truly interdisciplinary and knowing about general properties of networks allows students to see common patterns across disciplines, and thereby transcend disciplinary boundaries, said Hiroki Sayama, one of the partners on the project and Director of the Center for Collective Dynamics of Complex Systems and Associate Professor of Systems Science and Industrial Engineering at Binghamton University. It would be wonderful to see students studying various subjects - languages, history, social phenomena, biological organisms, engineered products, the Internet - all from a common lens of networks.

Porter, Sayama, and co-authors Catherine Cramer, Lori Sheetz, and Stephen Uzzo enumerated seven key concepts (with the input of numerous others) that characterise networks. The work was driven by one key question: what should every person living in the 21st century know about networks by the time they finish secondary education? The sooner future scientists know these core ideas, the sooner they can make networks around us more efficient, cost-effective, and safe.

The booklet, called 'Network Literacy: Essential Concepts and Core Ideas', breaks down the key ideas so that teachers can use it in the classroom or for lesson planning. The concepts have comparable importances, and they are ordered roughly according to difficulty level: the earlier concepts are easier to understand for everyone, whereas the latter ones may need more thinking and learning to grasp fully what they mean.

The project was done in collaboration with the New York Hall of Science and the U.S. Military Academy at West Point. The booklet has been translated into eight different languages so far, including Persian, Japanese, and German. The booklet (including all translations) is freely available online. 

A paper (with Sayama as the lead author), called 'What Are Essential Concepts About Networks?', about the procedure of creating the booklet appeared on 11 November as an advance-access article in the Journal of Complex Networks.

 

If A is for Aperiodic Tiles what about B? Or C? And Z?

Today we launch our A-Z of Oxford Mathematics beginning with Roger Penrose's beguiling explanation of the paving outside the Andrew Wiles Building. Our alphabet is intended to give a flavour, letter by letter, of the depth of mathematical research and imagination at work in Oxford (and beyond). As well as the website we will create posters for printing for use in schools and beyond. 

M.C. Escher is known as the mathematician's (and hippie's) favourite artist. But why? And was Escher, a man who claimed he knew no mathematics, really a mathematical genius?

In this lecture Roger Penrose and Jon Chapman not only show why Escher has won the artistic and mathematical hearts of mathematicians, but also why his art is inspiring both artists and mathematicians today, as captured in Jon's brilliant updating of Escher's 'Picture Gallery' to the new mathematics building in Oxford.

Oxford University has today opened a new Data Science Lab in collaboration with Emirates. It will see experts from around the University use cutting-edge analysis to help the airline make its services more efficient and customer-focussed.

The new Lab will bring together researchers from at least five departments within the University, including the Mathematical Institute, the Oxford Internet Institute and the Departments of Engineering Science, Computer Science and Statistics. Joined by visiting Fellows from Emirates, the academics will work with the airline’s ever-growing datasets to help it understand its processes and customer preferences in greater detail. In turn, it will create new products and services, better suited to the needs of its passengers.

"In recent years, airlines have gained access to much more data than they had in the past — from the price of tickets they sell online to the music preferences of frequent flyers,” explains Peter Grindrod CBE, Professor of Mathematics at the University’s Mathematical Institute and Director of the new Lab. “In other sectors, we’ve already seen that businesses which become data-rich assume a more customer-focussed approach and now it’s the turn of the airlines. We’ll help Emirates fuse together data and analyse it in the right way, so they can create new services and operational advantages.”

The University will provide Emirates with a wide-ranging pool of expertise in the form of mathematicians, scientists, engineers and social scientists. Emirates will provide industry expertise and the data itself — including information from its Skywards loyalty program. “At Oxford we have experts in all kinds of relevant areas — from optimisation and machine learning, to behavioural analytics and ethics,” continues Professor Grindrod.

In particular, researchers from the Mathematical Institute will investigate how to apply optimisation techniques to the Emirates data, and a team from Engineering Science will develop machine learning techniques that allow complex data sets to be interrogated quickly and efficiently. Meanwhile, social scientists from the Oxford Internet Institute will use behavioural analytics to understand the human aspects of the data. “It’s an exciting time for data science, with rapid advances in the techniques we use being applied to real problems that will have an impact on people’s lives,” adds Grindrod.

The new Lab — which was formally opened today by the President of Emirates, Sir Tim Clark, and Professor Grindrod — will be situated within the Mathematical Institute and form part of the Oxford Centre for Information. The partnership will last for five years.

Speaking at the Lab’s official launch at the University, Sir Tim Clark said: “In the age of the digital economy, we have witnessed first-hand how technology-based innovation can transform brands and disrupt entire industries by placing the customer at the heart of the business. The Oxford-Emirates Data Science Lab will provide us with a best-in-class dedicated team who can test and develop new business solutions using big data and real-time analytics, helping to the transform the Group into a customer-centric, travel experience company

Vortices do amazing things. They dance, they tie themselves in knots, they challenge mathematicians to explain them. In this case Étienne Ghys, CNRS Directeur de Recherche at the École Normale Supérieure de Lyon takes on the task of explaining.

Oxford Mathematics was pleased to host this lecture as part of the Clay Mathematics Institute’s 2015 Research Conference.

Étienne Ghys is the first recipient of the Clay Award for the Dissemination of Mathematical Knowledge.