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A life belt, a coffee cup, a jumping ball, a beach ball. What do these objects have in common? What sets them apart? Questions like these come under the mathematical umbrella of topology. And the theory of homology enables us to explore and understand them. Find out more in the latest in our Oxford Mathematics Alphabet.

Roger Heath-Brown is one of Oxford's foremost mathematicians. His work in analytic number theory has been critical to the advances in the subject over the past thirty years and garnered Roger many prizes.

As he approached retirement, Roger gave this interview to Ben Green, Waynflete Professor of Mathematics in Oxford and himself a leading figure in the field of number theory. In the interview Roger reflects on his influences, his achievements and the pleasures that mathematics has given him.
 

Oxford Mathematician and Charles Simonyi Professor for the Public Understanding of Science in the University of Oxford, Marcus du Sautoy, has been named one of London's most influential mathematicians in the London Standard Progress 1000 awards. The Progress 1000, in partnership with Citi, is an annual event hosted by The London Evening Standard to celebrate the people whose influence across many spheres of London life is felt most keenly by those who live in the City.

Marcus is not only a leading mathematician in his own right, but a driving force in the promotion and popularisation of mathematics and associated sciences. He has taken mathematics and science around the world, expressing its elegance, pleasures, and occasional pains, through lectures, theatre (his X & Y, a mathematical play written with Victoria Gould has been widely acclaimed) and most recently in his book "What We Cannot Know" where he tries to identify the frontiers to our knowledge. 

Alison Etheridge FRS, Professor of Probability in the University of Oxford, has been named Fellow of the Institute of Mathematical Statistics (IMS).  Professor Etheridge received the award for outstanding research on measure-valued stochastic processes and applications to population biology; and for international leadership and impressive service to the profession.

Each Fellow nominee is assessed by a committee of their peers for the award.  In 2016, after reviewing 50 nominations, 16 were selected for Fellowship.  Created in 1935, the Institute of Mathematical Statistics is a member organisation which fosters the development and dissemination of the theory and applications of statistics and probability. An induction ceremony took place on July 11 at the World Congress in Probability and Statistics in Toronto, Ontario, Canada.

Alison is also President Elect of the IMS.

This summer, about 200 teenagers will take part in mathematical summer schools hosted by Oxford Mathematics in the Mathematical Institute. Here is their story.
 
First to arrive were the 24 students from 15 countries across Europe who are taking part in PROMYS Europe, a six-week mathematical programme run by a partnership of PROMYS, the Mathematical Institute in Oxford, the Clay Mathematics Institute, and Wadham College, University of Oxford. As one student attending for the first time put it, "At PROMYS we do not learn Maths; we discover it. This gives us a much better understanding of the basics on which all other Maths is built".  

PROMYS has run in Boston, USA for more than 25 years, and this year sees the second occurrence of the new PROMYS Europe programme. Thanks to generous support from the organising partners and donors, selection for the programme is needs-blind, with partial and full financial support for those participants who would otherwise not be able to attend. The super-keen students are joined this summer by 7 undergraduate 'counsellors', also from across Europe (and including two current Oxford students), with teaching from Glenn Stevens (Boston University), Henry Cohn (Microsoft Research), Vicky Neale (Oxford) and David Conlon (Oxford), and guest lectures by mathematicians from Oxford and beyond. One counsellor, who also attended PROMYS as a student, observed "Three years ago, when I entered the PROMYS family, I learned one of the most important lessons - one should be taught how to think, not what to think - and this is exactly what this program does."
 
The Andrew Wiles Building is an ideal venue for hosting summer schools such as these, and indeed with careful planning can accommodate not one but three simultaneous events. The university's one-week UNIQ summer schools are for UK students about to enter their final year at school, to give them a taste of what it is like to study at Oxford, with priority being given to applicants from low socio-economic backgrounds and/or from areas with low progression to higher education. Demand for mathematics and statistics is high, and this year Rebecca Cotton-Barratt, the Schools Liaison Officer and Admissions Coordinator in the Mathematical Institute, and Mareli Grady, the Schools Liaison Officer in the Statistics Department, have between them coordinated three UNIQ summer schools, giving over 80 students the inspiring experience of studying Mathematics in Oxford. Reflecting at the end of the week, students commented "I thought I wasn’t good enough to apply but I will be applying now as I have gained more confidence", and "really enjoyable with lots of variety in various fields", and, interestingly, "I don’t want to go home now".
 
Later in the summer, we are looking forward to welcoming two summer schools organised by the UK Mathematics Trust. The National Mathematics Summer School and Summer School for Girls are each for around 40 students aged 15 and 16, invited to participate on the basis of their outstanding performance in national mathematics competitions. They give students a taste of mathematics beyond the school curriculum, as well as exploring more familiar material in depth, with an emphasis on problem solving and collaborative work. The teams of staff leading these summer schools include alumni, students and staff from Oxford Mathematics, and we are delighted to host these events.

All in all, the schools demonstrate that there is a passion for the subject of mathematics, a passion Oxford and its partners are keen to nurture for the long-term educational, scientific and economic benefits it will bring. 

Photo courtesy of Wadham College.

Oxford Mathematician Dominic Joyce FRS has won the 2016 LMS (London Mathematical Society) Fröhlich Prize "for his profound and wide-ranging contributions to differential and algebraic geometry." Dominic is Professor of Mathematics and Senior Research Fellow at Lincoln College. His research is, in his own words, "mostly in Differential Geometry, with occasional forays into some more esoteric areas of Theoretical Physics."

Oxford Mathematician James Maynard has been awarded a European Mathematical Society Prize at the 7th European Congress of Mathematics in Berlin. The prizes are awarded every four years in recognition of excellence in mathematics to ten individuals under the age of 35 living or working in Europe.

In the words of the judges James was awarded the prize for "his remarkable and deep results in analytic number theory, dealing especially with the distribution of primes. He is recognised in particular for his new proof, with improved estimates, of the 'small gaps between the primes theorem'."

In addition to James, Geordie Williamson, formerly a researcher in Oxford Mathematics was also awarded a prize for his "fundamental contributions to the representation theory of Lie algebra and algebraic groups, including his proof of Seorgel's conjecture on bimodules associated to Coxeter groups, and his startling counterexamples to the expected bounds in Lustig's conjecture on the characters of rational representations of algebraic groups." 

Vicky Neale from Oxford Mathematics has won an MPLS (Mathematical, Physical and Life Sciences) Teaching Award for her innovative and entertaining undergraduate teaching. Using blogs and tips to back up her lectures, Vicky's expansive approach has led to widespread praise from the toughest of critics, namely the students themselves.

Vicky is Whitehead Lecturer at Oxford, a post dedicated to the wider communication of mathematics. She regularly gives public lectures, including the prestigious London Mathematical Society Popular Lectures in 2013 and runs workshops for schools and teenagers including PROMYS Europe. She is also a regular guest on radio including BBC Radio 4's' Start the Week' and 'In Our Time'.

The MPLS awards are part of the University of Oxford's commitment to the highest standards of teaching across all its departments. 

How can we explain the patterns of genetic variation in the world around us? The genetic composition of a population can be changed by natural selection, mutation, mating, and other genetic, ecological and evolutionary mechanisms. How do they interact with one another, and what was their relative importance in shaping the patterns we see today? 

In our latest Oxford Mathematics Public Lecture Alison Etheridge FRS, Professor of Probability in the University of Oxford explores the remarkable power of simple mathematical caricatures in interrogating modern genetic data.

Oxford Mathematician Heather Harrington will be giving the London Mathematical Society (LMS) Popular Lectures this summer in London on 29 June and in September in Birmingham. The Lectures present exciting topics in mathematics and its applications to a wide audience and feature two lecturers who have been chosen for their mathematical distinction and communication skills.  

Heather's talk will be titled "the Shape of Data in Biology' and will focus on how computational developments in abstract mathematics can provide new insights in to the vast amounts of data generated by biological systems. The lectures are free but booking is required.