Tuesday, 14 November 2017

Andrew Dancer elected to the Council of the LMS

Oxford Mathematician Andrew Dancer has been elected to the Council of the London Mathematical Society (LMS).  The Society publishes books and periodicals, organises mathematical conferences, provides funding to promote mathematical research and education and awards a number of prizes and fellowships for excellence in mathematical research.

Andrew Dancer's research focuses on Differential Geometry, especially the study of Einstein spaces. His recent work on Ricci flows features in our latest case-studies series.

Andrew is a Fellow of Jesus College here in Oxford.



Monday, 13 November 2017

Mathematics tracks the flu. Julia Gog Oxford Mathematics Public Lecture now online

Can mathematics really help us in our fight against infectious disease? Join Julia Gog as she explores some exciting current research areas where mathematics is being used to study pandemics, viruses and everything in between, with a particular focus on influenza.

Julia Gog is Professor of Mathematical Biology, University of Cambridge and David N Moore Fellow at Queens’ College, Cambridge.






Friday, 10 November 2017

James Maynard appointed Research Professor and receives a Wolfson Merit Award from the Royal Society

Oxford Mathematician James Maynard has been appointed Research Professor and receives a Wolfson Merit Award from the Royal Society. The Royal Society Wolfson Merit Award is a prestigious award intended to attract or retain respected scientists of outstanding achievement and potential.

Professor Maynard's project, 'Structure in the primes, with applications', aims to develop techniques to understand the statistical properties of the distribution of prime numbers - a central problem in number theory. The project consists of three large projects to be investigated over a five-year period. The projects follow the common theme of studying classical problems in analytic number theory by attempting to classify counter-examples, should they exist. This approach has been remarkably successful in analytic arguments, and is an example of a common connection between analysis, combinatorics and algebra. The underlying techniques also provide flexible and universal means of answering rigorously many real-world questions about primes.

James Maynard is one of the brightest young stars in world mathematics at the moment, having made dramatic advances in analytic number theory in the years immediately following his 2013 doctorate. These advances have brought him worldwide attention in mathematics and beyond. Just 30, he has already gained many markers of distinction, including the European Mathematical Society Prize, the Ramanujan Prize and the Whitehead Prize. He will be an invited speaker at the quadrennial International Congress of Mathematicians in 2018. He also holds a Clay Research Fellowship (2013-18), the most prestigious early career position in world mathematics.

Friday, 10 November 2017

Thaleia Zariphopoulou appointed as a Visiting Professor in the Mathematical Institute

We are delighted to announce that Thaleia Zariphopoulou has been appointed as a Visiting Professor in the Mathematical Institute, University of Oxford for three years from 1st November 2017.

Thaleia holds the Presidential Chair in Mathematics and is the V. H. Neuhaus Centennial Professor at the University of Texas at Austin. From 2009-2012 she was the Oxford-Man Professor of Quantitative Finance here in Oxford and has remained in close contact with colleagues in the Mathematical Institute.

Thaleia's works spans financial mathematics, notably stochastic optimization and quantitative finance. She has held many visiting fellowships and in 2012 became a Fellow of the Society for Industrial and Applied Mathematics (SIAM) "for contributions to stochastic control and financial mathematics."

Wednesday, 1 November 2017

Looking for a PhD in mathematics? And some funding?

Oxford Mathematics now has up to 50 fully-funded studentships available each year for doctoral degrees. All home, EU and overseas  applicants are eligible to apply – up to 20 studentships each year will be available to applicants regardless of nationality.

Find out more about postgraduate study and research life in Oxford.



Wednesday, 1 November 2017

Oxford Mathematics introduces its new Master's in Mathematical Sciences

The Oxford Master’s in Mathematical Sciences (or 'OMMS') is now admitting students to start in October 2018.  This new master’s degree is run jointly by the Mathematical Institute and the Department of Statistics at the University of Oxford.  For the first time we are able to offer students from across the world a masters course that draws on the full range of our research across the mathematical sciences, from fundamental themes in the core to interdisciplinary applications.

This MSc complements a range of other masters’ courses at Oxford - each of which has distinctive features and meets a specialised need.  Click for further details of mathematics and statistics courses at Oxford.

Tuesday, 24 October 2017

Closing the Gap: the quest to understand prime numbers - Vicky Neale's Oxford Mathematics Public Lecture now online

Prime numbers have intrigued, inspired and infuriated mathematicians for millennia and yet mathematicians' difficulty with answering simple questions about them reveals their depth and subtlety.

Vicky Neale describes recent progress towards proving the famous Twin Primes Conjecture and explains the very different ways in which these breakthroughs have been made - a solo mathematician working in isolation, a young mathematician displaying creativity at the start of a career, a large collaboration that reveals much about how mathematicians go about their work.

Vicky Neale is Whitehead Lecturer at the Mathematical Institute, University of Oxford and Supernumerary Fellow at Balliol College.





Monday, 23 October 2017

How to make sense of our digital conversations

For many years networks have been a fruitful source of study for mathematicians, one of the first notable examples of network analysis being Leonard Euler's study of paths on the Königsberg bridges. Since that time the field of graph theory and network science has developed greatly and the problems we want to model have also changed. 

Perhaps the most evident modern-day networks are those of online social networks such as Facebook, Twitter, and Instagram. Unlike the networks of the Königsberg bridges which are literally set in stone, the networks of interactions and friendships between users of these networks can grow and disappear within minutes or hours. This means we need to develop new tools and algorithms to be able to analyse them fully. 

Working with the data-focused Bloom Agency, Oxford Mathematician Andrew Mellor's goal is to analyse, in real time, the conversations occurring on social media surrounding brands, ideas, and reaction to real world events and television shows. To do this he developed the temporal event graph, a static representation of a temporal network. In the temporal event graph our interactions are now nodes, and interactions are linked if they share participants and occur close together in time. Looking at temporal networks in this way captures both the topology of the interactions between agents and the timings between these connections. This complex interplay between topology and temporal connectivity has a profound effect on the spread of epidemics (or viral content) on the network. We can use methods derived for static networks to efficiently analyse the network. These methods are not restricted to the digital domain and can in fact be applied to any sequence of interactions such as flight and transport networks, brain networks, and proximity networks.

Returning to the original application, Andrew and colleagues are currently using the temporal event graph to understand how conversations evolve online, how a user's behaviour changes depending on the conversational topic, and to classify the zoo of conversation types that have been observed. This gives a unique insight into how we behave online, and gives new methods of characterising behaviour as a function of time. 

Thursday, 19 October 2017

Dominic Vella wins Philip Leverhulme Prize

Oxford Mathematician Dominic Vella has won one of this year's prestigious Philip Leverhulme Prizes. The award recognises the achievement of outstanding researchers whose work has already attracted international recognition and whose future career is exceptionally promising.

Dominic's research is concerned with various aspects of solid and fluid mechanics in general but with particular focus on the wrinkling of thin elastic objects and surface tension effects. You can see him discussing his work here.

Monday, 16 October 2017

Exploring Steiner Chains with Möbius Transformations

Oxford Mathematician Kristian Kiradjiev has been awarded the Institute of Mathematics and its Applications (IMA) Early Career Mathematicians Catherine Richards Prize 2017 for his article on 'Exploring Steiner Chains with Möbius Transformations.' Here he explains his work.

"A beautiful example that one encounters in the geometry of circles is the so-called Steiner chains, named after the Swiss mathematician Jacob Steiner. A Steiner chain is defined as a chain of $n$ circles, each tangent to the previous one and the next one, and also to two given non-intersecting circles, which we will call bounding circles. We focus exclusively on Steiner chains, one of whose bounding circles lies within the other, although the concept also exists when the bounding circles are disjoint. We also define a closed Steiner chain to be such that the first and last circles of the chain are tangent to each other. For the sake of simplicity, we will limit ourselves to simple closed chains, i.e. wrapping only once around the inner bounding circle, although, again, one can have multi-cyclic closed chains, which wrap around several times before touching the first circle.

One of the main results, concerning Steiner chains is known as Steiner's porism. A porism is a mathematical proposition, which nowadays usually refers to a statement that is either not true, or is true and holds for an infinite number of values, provided a certain condition is satisfied (cf. Poncelet's porism). Steiner's porism states that given two bounding circles and the first circle from the chain, if a Steiner chain exists, then there are infinitely many of them, irrespective of the position of the first circle.

A lot of other fascinating properties have been discovered. For example, it is known that the centres of the circles in the chain lie either on an ellipse (or circle) when one of the bounding circles lies within the other, or on a hyperbola if not. Also, the points of tangency between the circles in the chain happen to lie on a circle. More interestingly, using inversion (and the inversive distance invariant), a feasibility criterion has been established for whether a closed Steiner chain is supported for a given $n$ and a pair of bounding circles. The problem I considered is somewhat the opposite: given $n$ positive numbers, does there exist a pair of bounding circles such that we can arrange $n$ circles with radii the given $n$ numbers in a simple closed Steiner chain between these bounding circles? This can also be reformulated as a geometrical problem of inscribing and circumscribing circles around a chain of touching circles with given radii. In order to answer this question, I essentially relied on the concept of Möbius transformations, which are conformal maps (i.e. preserve angles) in the extended complex plane $\widetilde{\mathbb{C}}=\mathbb{C}\cup\{\infty\}$ of the form \begin{equation*} f(z)=\frac{az+b}{cz+d}, \label{eq:1} \end{equation*} where $z\in\widetilde{\mathbb{C}}$, and $a,b,c,d\in\mathbb{C}$ with $ad-bc\neq 0$ (so as to avoid constant maps). We note that translation, scaling, and inversion are particular cases of Möbius transformations. What is really useful about them, is that they map circlines (circles or lines) to circlines. As a result, I managed to derive a set of criteria on the $n$ radii for when they can form a Steiner chain. In addition, if such a chain exists, I gave a method how to construct it.

There is a number of generalisations, of which the Soddy's hexlet, which can be thought of as a 3D analogue of a Steiner chain, is a beautiful example and is such that the envelope of the touching spheres is the Dupin cyclide, an inversion of the torus."

The three rotating figures above show: a simple closed Steiner chain with 7 circles, Soddy’s Hexlet and Dupin Cyclide.