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.
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.
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.
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.
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.
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 Giles, Richard Haydon, Peter Keevash, Jochen 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.
Oxford Mathematicians Ruth Baker and Alex Scott have been awarded Leverhulme Research Fellowships. Ruth, a mathematical biologist, has been given her award to further her research in to efficient computational methods for testing biological hypotheses while Alex, who works in the areas of combinatorics, probability, and algorithms, will be working on interactions between local and global graph structure.
The Leverhume Research Fellowships are given to experienced researchers, particularly those who are or have been prevented by routine duties from completing a programme of original research.
From Bach’s Goldberg Variations to Schoenberg’s Twelve-tone rows, composers have exploited symmetry to create variations on a theme. But symmetry is also embedded in the very way instruments make sound. Marcus du Sautoy shares his passion for music, mathematics and their enduring and surprising relationship. The lecture culminates in a reconstruction of nineteenth-century scientist Ernst Chladni's exhibition that famously toured the courts of Europe to reveal extraordinary symmetrical shapes in the vibrations of a metal plate.
Marcus du Sautoy is Charles Simonyi Professor for the Public Understanding of Science at Oxford University.
Oxford Mathematics's Professor Andrew Wiles has been awarded the Copley Medal, the Royal Society's oldest and most prestigious award. The medal is awarded annually for outstanding achievements in research in any branch of science and alternates between the physical and biological sciences.
Andrew Wiles is one of the world's foremost mathematicians. His proof of Fermat's Last Theorem in the 1990s catapulted him to unexpected fame as both the mathematical and the wider world were gripped by the solving of a 300 year-old mystery. In 1637 Fermat had stated that there are no whole number solutions to the equation $x^n + y^n = z^n$ when n is greater than 2, unless xyz=0. Fermat went on to claim that he had found a proof for the theorem, but said that the margin of the text he was making notes on was not wide enough to contain it.
After seven years of intense study in private at Princeton University, Andrew announced he had found a proof in 1993, combining three complex mathematical fields – modular forms, elliptic curves and Galois representations. However, he had not only solved the long-standing puzzle of the Theorem, but in doing so had created entirely new directions in mathematics, which have proved invaluable to other scientists in the years since his discovery.
Educated at Merton College, Oxford and Clare College, Cambridge, where he was supervised by John Coates, Andrew made brief visits to Bonn and Paris before in 1982 he became a professor at Princeton University, where he stayed for nearly 30 years. In 2011 he moved to Oxford as a Royal Society Research Professor. Andrew has won many prizes including, in 2016, the Abel Prize, the Nobel Prize of mathematics. He is an active member of the research community at Oxford, where he is a member of the eminent number theory research group. In his current research he is developing new ideas in the context of the Langlands Program, a set of far-reaching conjectures connecting number theory to algebraic geometry and the theory of automorphic forms.
Meteorologist Ed Lorenz was one of the founding fathers of chaos theory. In 1963 he showed with just three simple equations that the world around us could be both completely deterministic and yet practically unpredictable. In the 1990s, Lorenz’s work was popularised by science writer James Gleick who used the phrase “The Butterfly Effect” to describe Lorenz’s work. The notion that the flap of a butterfly’s wings could change the course of weather was an idea that Lorenz himself used. However, he used it to describe something much more radical - he didn’t know whether the Butterfly Effect was true or not.
In this lecture Tim Palmer discusses Ed Lorenz the man and his work, and compares and contrasts the meaning of the “Butterfly Effect" as most people understand it today, and as Lorenz himself intended it to mean.
Tim Palmer is Royal Society Research Professor in Climate Physics at the University of Oxford.
