Monday, 10 July 2017

Oxford Mathematicians win outstanding certificate as part of the new IIF Tao Hong Award

Oxford Mathematicians Stephen Haben and Peter Grindrod and colleagues have won an outstanding certificate as part of the new IIF Tao Hong Award for papers in energy forecasting published in the International Journal of Forecasting.

The paper, 'A new error measure for forecasts of household-level, high resolution electrical energy consumption,' provides high-quality verification tools for load forecasts, which are essential in managing power systems. This is particularly helpful for work on demand profiling in the residential sector, where the temporal resolution of data has increased rapidly in recent years.

Monday, 10 July 2017

Shapes and Numbers - Oxford Mathematics Research considers number theory and topology

As part of our series of research articles deliberately focusing on the rigour and intricacies of mathematics, we look at Oxford Mathematician Minyhong Kim's research in to the relationship between number theory and topology. Minhyong Kim is Professor of Number Theory here in Oxford and Fellow of Merton College.

It is probably well-known that number theory is the source of some of the oldest and most accessible questions in mathematics:

Which regular polygons can be constructed using only a straight-edge and a compass?

How are the primes distributed in the large?

What are the integral solutions of the equation $x^n+y^n=z^n$?

Is there an algorithm to generate the rational solutions to rational cubic equations of the form $y^2=x^3+ax+b$?

Many people with mathematical inclinations will be drawn to the natural simplicity of these queries, perhaps early on in life, and will gradually expand the reservoir of their knowledge in the hope of approaching a solution, progressing from the easy to the hard cases. Mathematics as a whole has had a historical relationship to number theory parallel to the personal development of a mathematician. Over millennia, logic, algebra, analysis, and geometry have all been employed in the service of number theory, the tools of the trade often becoming more powerful or refined in response to the demands of arithmetic problems. In our times, it's difficult to find a single area of mathematics, from the elementary to the most conceptually sophisticated, which is not used in some serious way in number theory. Number theory has acquired thereby the status of a quite general testing ground for conceptual progress: a mysterious and abstract theory can prove its worth and its connection to mathematical reality by its applicability to concrete problems of number theory. The tendency to generate natural problems has enabled number theory to reconstitute itself as a pure laboratory for the power of ideas.

Since the 1960s, a major instance of this interaction has been that between topology and number theory. Topologists are adept at coming up with extremely abstruse notions of shape and space, such as a topos, a simplicial set, or a spectrum. Each of these in turn have had fruitful number-theoretic incarnations in the study of equations over finite fields, quadratic forms, and in the Galois theory of $p$-adic fields. Minhyong Kim's research continues the exploration of the relationship between topology and number theory, most actively with ideas from homotopy theory. As an elementary example, consider a set of paths $P(1 ,z)$ in the punctured complex plane from point $1$ to the point $z$. Surprisingly, there is a big difference in structure between the path spaces with $z$ transcendental and those with $z$ algebraic. More precisely, in the latter case, the homotopy classes of paths, suitably completed, admit an intricate symmetry group coming from Galois theory. Kim has been studying the classification of such hidden symmetry with a view to detecting rational or algebraic solutions to polynomial equations. For example, using only the Galois symmetries of the path spaces between solution points, he has been able to reprove the theorem, first proved by Faltings then vastly improved by Wiles, that the equation $$x^n+y^n=1$$ has only finitely many rational solutions when $n\geq 4$ (this is joint work with John Coates).

Most recently, in collaboration with many mathematicians and physicists from the US, Europe, and Asia, Kim is involved in a programme to develop the ideas of topological quantum field theory in the realm of number theory. The main mathematical impact of topological quantum field theory arises from the use of an integral over fields (in the sense of the physicist, not that of the algebraist) to measure the quantum correlation between points on a space, the winding of knots, or to define a numerical invariant of the space itself. The current project explores the application of this idea to primes and rings of integers in number fields (now in the sense of algebraists), where the role of the physical field is played by representations of arithmetic Galois groups. These representations themselves lie at the crossroads of the most important paths of investigation in present day number theory, such as the conjecture of Birch and Swinnerton-Dyer, the theory of zeta and L-functions, and the Langlands programme. One goal of this research is to understand their centrality from a point of view consistent with the intuition of geometry, topology, and physics.

Friday, 7 July 2017

The Law of the Few - Sanjeev Goyal's Oxford Mathematics Public Lecture now online

The study of networks offers a fruitful approach to understanding human behaviour. Sanjeev Goyal is one of its pioneers. In this lecture Sanjeev presents a puzzle:

In social communities, the vast majority of individuals get their information from a very small subset of the group – the influencers, connectors, and opinion leaders. But empirical research suggests that there are only minor differences between the influencers and the others. Using mathematical modelling of individual activity and networking and experiments with human subjects, Sanjeev helps explain the puzzle and the economic trade-offs it contains.

Professor Sanjeev Goyal FBA is the Chair of the Economics Faculty at the University of Cambridge and was the founding Director of the Cambridge-INET Institute.




Thursday, 6 July 2017

Alex Wilkie and Alison Etheridge win LMS Prizes

Congratulations to the Oxford Mathematicians who have just been awarded LMS prizes. Alex Wilkie receives the Pólya Prize for his profound contributions to model theory and to its connections with real analytic geometry and Alison Etheridge receives the Senior Anne Bennett Prize in recognition of her outstanding research on measure-valued stochastic processes and applications to population biology; and for her impressive leadership and service to the profession.

Thursday, 29 June 2017

Oxford Mathematics Visiting Professor Michael Duff awarded the Paul Dirac Medal and Prize

Professor Michael Duff of Imperial College London and Visiting Professor here in the Mathematical Institute in Oxford has been awarded the Dirac Medal and Prize for 2017 by the Institute of Physics for “sustained groundbreaking contributions to theoretical physics including the discovery of Weyl anomalies, for having pioneered Kaluza-Klein supergravity, and for recognising that superstrings in 10 dimensions are merely a special case of p-branes in an 11-dimensional M-theory.”

Michael Duff holds a Leverhulme Emeritus Fellowship, is a Fellow of the Royal Society, the American Physical Society and the Institute of Physics and was awarded the 2004 Meeting Gold Medal, El Colegio Nacional, Mexico. 

Wednesday, 21 June 2017

Exploding the myths of Ada Lovelace’s mathematics

Ada Lovelace (1815–1852) is celebrated as “the first programmer” for her remarkable 1843 paper which explained Charles Babbage’s designs for a mechanical computer. New research reinforces the view that she was a gifted, perceptive and knowledgeable mathematician.

Christopher Hollings and Ursula Martin of Oxford Mathematics, and Adrian Rice, of Randolph-Macon College in Virginia, are the first historians of mathematics to investigate the extensive archives of the Lovelace-Byron family, held in Oxford’s Bodleian Library. In two recent papers in the Journal of the British Society for the History of Mathematics and in Historia Mathematica they study Lovelace’s childhood education, where her passion for mathematics was complemented by an interest in machinery and wide scientific reading; and her remarkable two-year “correspondence course” on calculus with the eminent mathematician Augustus De Morgan, who introduced her to cutting edge research on the nature of algebra.

The work challenges widespread claims that Lovelace’s mathematical abilities were more “poetical” than practical, or indeed that her knowledge was so limited that Babbage himself was likely to have been the author of the paper that bears her name. The authors pinpoint Lovelace’s keen eye for detail, fascination with big questions, and flair for deep insights, which enabled her to challenge some deep assumptions in her teacher’s work. They suggest that her ambition, in time, to do significant mathematical research was entirely credible, though sadly curtailed by her ill-health and early death.

The papers, and the correspondence with De Morgan, can be read in full on the website of the Clay Mathematics Institute, who supported the work, as did the UK Engineering and Physical Sciences Research Council.

Monday, 19 June 2017

Live Podcast and Facebook. The Law of the Few - Sanjeev Goyal's Oxford Mathematics Public Lecture 28 June

The study of networks offers a fruitful approach to understanding human behaviour. Sanjeev Goyal is one of its pioneers. In this lecture Sanjeev presents a puzzle:

In social communities, the vast majority of individuals get their information from a very small subset of the group – the influencers, connectors, and opinion leaders. But empirical research suggests that there are only minor differences between the influencers and the others. Using mathematical modelling of individual activity and networking and experiments with human subjects, Sanjeev helps explain the puzzle and the economic trade-offs it contains.

Professor Sanjeev Goyal FBA is the Chair of the Economics Faculty at the University of Cambridge and was the founding Director of the Cambridge-INET Institute.

Podcast notification - 5pm on 28 June 2017

Oxford University Facebook

Places still available if you wish to attend in person - Mathematical Institute, Oxford, 28 June, 5pm. Please email to register

Saturday, 17 June 2017

Oxford Mathematician Alison Etheridge awarded an OBE

Oxford Mathematician Alison Etheridge FRS has been awarded an OBE in the Queen's Birthday Honours List for Services to Science. Alison is Professor of Probability in Oxford and will take up the Presidency of the Institute of Mathematical Statistics in August 2017.

Alison's research has a particular focus on mathematical models of population genetics, where she has been involved in efforts to understand the effects of spatial structure of populations on their patterns of genetic variation. She recently gave an Oxford Mathematics Public Lecture on the mathematical modelling of genes.

Friday, 16 June 2017

Oxford Mathematicians invited to speak at ICM 2018

The International Congress of Mathematicians (ICM) is the largest conference in mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU) and hands out the most important prizes in the subject, notably the Fields Medals and the Nevanlinna and Gauss Prizes. At the Congress leading mathematicians are invited to present their research and in 2018 in Rio Oxford Mathematics will be represented by Mike GilesRichard HaydonPeter KeevashJochen Koenigsmann, James Maynard and Miguel Walsh, a team whose wide-ranging interests demonstrate both the strength of the subject in Oxford, but also the scope of mathematics in the 21st Century.

Miguel and James are also Clay Research Fellows. The Clay Mathematics Institute supports the work of leading researchers at various stages of their careers and organises conferences, workshops, and summer schools. The annual Research Award recognises contemporary breakthroughs in mathematics.

If you want to know more about the ICM, Oxford Mathematician Chris Hollings explains how even mathematics cannot escape politics.

Tuesday, 13 June 2017

How fast does the Greenland Ice Sheet move?

Governments around the world are seeking to address the economic and humanitarian consequences of climate change. One of the most graphic indications of warming temperatures is the melting of the large ice caps in Greenland and Antarctica.  This is a litmus test for climate change, since ice loss may contribute more than a metre to sea-level rise over the next century, and the fresh water that is dumped into the ocean will most likely affect the ocean circulation that regulates our temperature.

Melting ice is not itself a sign of climate warming, because the ice sheet is constantly being replenished by new snow falling on its surface. The net amount of ice loss in fact results from a quite delicate imbalance between the addition of new snow and the discharge of ice to the ocean in the form of icebergs.  Understanding this imbalance requires an understanding of how fast the ice moves.   

Oxford Mathematician Ian Hewitt has been addressing this question using fluid-dynamical models. “We model glacial ice as a non-Newtonian viscous fluid. The central difficulty in computing the ice flow is the boundary condition at the base.  In conventional fluid mechanics a no-slip condition would apply, but the presence of melt water that has penetrated through cracks in the ice acts as a lubricant and effectively allows slip - often a very significant amount of slip.”   

In a recent study Ian has combined a model of the ice flow with a model for the water drainage underneath the ice to account for this varying degree of lubrication. "This new model is able to explain seasonal variations in the flow of the ice that have been observed using GPS instruments - it moves faster during spring and early summer, and slows down slightly in autumn.  Intriguingly, the net effect on the ice motion over the course of the year can be both positive and negative, depending on which of these - the acceleration or subsequent deceleration - dominates.  This depends on the amount of melt water that is produced on the surface, which has almost doubled over the last decade.”  

Ongoing work is attempting to combine the modelled behaviour with satellite observations to better constrain what might happen in the future.  Ian Hewitt talks about this research in an Oxford Sparks podcast.