Oxford Mathematics Public Lecture: Signatures of Streams - Terry Lyons

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Wednesday 2 November, 5 pm, Mathematical Institute, Oxford

A calculator processes numbers without caring that these numbers refer to items in our shopping, or the calculations involved in designing an airplane. Number without context is a remarkable abstraction that we learn as infants and which has profoundly affected our world.

Our lives start, progress in complex ways, and are finally complete. So do tasks executed on a computer. Multimodal streams are a pervasive “type”, and even without fixing the context, have a rich structure. Developing this structure leads to wide-ranging tools that have had award-winning impact on methodology in health care, finance, and computer technology.

Terry Lyons is Professor of Mathematics in Oxford and a Fellow of St Anne's College. His research is supported through the DataSig and Cimda-Oxford programmes. 

Please email @email to register.

The lecture will be available on our Oxford Mathematics YouTube Channel on 09 November at 5 pm.

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

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Introduction to University Mathematics - watch now

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In their first two weeks of their first term - which started just last week - Oxford Mathematics Undergraduates take the 'Introduction to University Mathematics' course, introducing them to the concepts and ways of mathematical thinking that they will use in the years ahead. Much of the context will be familiar from high school but the way we think and write about it at university, and construct arguments and proofs, is more rigorous. In summary it is a recap and a pointer to what is to come for our students.

We are showing the whole course over eight lectures over the next few weeks to help aspiring students whatever their ambition or destination. This is Lecture 1. Some of the accompanying materials (slides and problem sheets) are publicly available here

Dip in as you wish; and enjoy


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Oxford Mathematician Kaibo Hu wins SIAM Early Career Prize

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Kaibo Hu has been awarded the SIAM Early Career Prize in Computational Science and Engineering for "contributions to the finite element exterior calculus, particularly structure-preserving numerical algorithms for magnetohydrodynamics.”

Kaibo is Royal Society University Research Fellow in Oxford Mathematics and Christ Church College. He works on numerical PDEs, particularly finite element exterior calculus, a framework that preserves topological and geometric structures of continuous problems in numerical computation. His recent results include applications of the Bernstein-Gelfand-Gelfand resolution as a systematic approach for analysing and discretising PDEs, with potential applications to geometry, continuum mechanics and numerical general relativity. 

Kaibo will be awarded the prize at the 2022 SIAM Conference on Computational Science and Engineering (CSE23), scheduled to take place February 26 – March 3, 2023 in Amsterdam, The Netherlands where he will give a plenary lecture.

Established in 2016, the prize is awarded every two years to one post-PhD early career researcher in the field of computational science and engineering for outstanding, influential, and potentially long-lasting contributions to the field within seven years of receiving the PhD or equivalent degree as of January 1 of the award year.

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Oxford Mathematics joins Martingale Postgraduate Foundation programme

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Oxford Mathematics is delighted to be a partner in the Martingale Postgraduate Foundation's programme of scholarships for students wishing to pursue postgraduate studies in STEM (Science, Technology, Engineering, and Mathematics) subjects.

Martingale is a new postgraduate foundation that offers full funding and multi-year support for outstanding UK students to complete STEM PhDs at leading UK research universities. The first cohort will be concentrated on mathematics.

In today’s modern job market, particularly in STEM, postgraduate degrees are now increasingly required for academic and career advancement. According to the UK Commission for Employment and Skills Report, there is an annual shortfall of 40,000 STEM skilled workers and demand is expected to increase in the future. For many students, financial costs are a significant barrier to postgraduate education. Student loans alone are inadequate in covering tuition fees, especially when taking into account the rising cost of living.    

To address this, Martingale Scholars will receive funding for the full cost of a master’s and a PhD course. The scholarship will also include a full cost of living allowance, as well as an additional budget for research activities. The foundation will prioritise students for whom family income has been or would be a barrier to postgraduate education.

For its first cohort, Martingale is partnering with five leading research universities in the UK to provide scholarships in select master’s and PhD programmes in mathematics: the University of Cambridge, Imperial College London, King’s College London, the University of Oxford, and University College London. The foundation plans to expand its scholarships to other STEM subjects and universities in the next few years.

In addition to having their tuition fees fully funded by Martingale, Scholars will also receive access to outstanding career development opportunities. This includes attending leadership events and residentials, internships and industry placements, as well as opportunities to contribute to public engagement projects. Scholars will join a community of researchers and a network of leading universities and businesses across the UK.

For its first year, Martingale Foundation is looking for a cohort of scholars at each university who wish to pursue their postgraduate studies and research in mathematics, commencing in September 2023.

James Sparks, Head of the Mathematical Institute in Oxford, said: 

"The mathematical sciences are fundamental to UK industry, the economy, as well as mathematical and scientific progress in general. It's vital that we continue to fund and support the next generation of talented mathematics graduate students, whatever their background. The Mathematical Institute is delighted to be partnering with the Martingale Postgraduate Foundation to help ensure that outstanding students have the financial means to pursue graduate study at Oxford, and that talent isn't lost because of personal or family financial circumstances."

Applications will open today, 6th October. Undergraduates in mathematics who are in their final year, as well as recent graduates, are encouraged to apply for the Martingale scholarship.

Applications are welcome from candidates from all backgrounds, especially those for whom family income has been, or would be, a barrier to postgraduate education. Candidates must also be able to demonstrate both academic excellence and a passion for their area of research. More information about eligibility and criteria can be found here and also on the Martingale Foundation website

The Martingale Foundation is a part of Ark Ventures, one of the country’s leading education charities. It is proudly supported by world-leading algorithmic trading company XTX Markets, whose generosity has helped make these scholarships possible.

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Oxford Mathematics Public Lecture: The million-dollar shuffle: symmetry and complexity - Colva Roney-Dougal

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Oxford Mathematics Public Lecture

The million-dollar shuffle: symmetry and complexity - Colva Roney-Dougal
Wednesday 5th October 2022
5.00-6.00pm, Mathematical Institute, Oxford

In 1936, Alan Turing proved the startling result that not all mathematical problems can be solved algorithmically. For those which can be, we still do not always know when there's a clever technique which could give us the answer quickly. In particular, the famous "P = NP" question asks whether, for problems where the correct solution has a proof which can easily be checked, in fact there's a quick way to find the answer.

Many difficult problems become easier if they have symmetries: finding the shortest route to deliver many parcels would be easy if all the houses were neatly arranged in a circle. This lecture will explore the interactions between symmetry and complexity.

Colva Roney-Dougal is Professor of Pure Mathematics at the University of St Andrews and Director of the Centre for Interdisciplinary Research in Computational Algebra.

Please email @email to register.

The lecture will be available on our Oxford Mathematics YouTube Channel on 12 October at 5 pm.

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

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Vicky Neale to become President of the Mathematical Association

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Congratulations to Vicky who will take up the position in 2024. Vicky  is the Whitehead Lecturer at the Mathematical Institute and Balliol College and also a Supernumerary Fellow at Balliol College.

Alongside her teaching, Vicky's role is to discuss mathematics with a broader audience via public lectures, talks and workshops in schools as well as mathematical summer schools for teenagers, notably PROMYS Europe for which she is Executive Director.

Vicky also enjoys  mathematical craft of various types and has written two books, Why Study Mathematics? and Closing the Gap: the quest to understand prime numbers.

The Mathematical Association exists to support and promote confidence and enjoyment in mathematics for all, by interacting with teachers and those with an interest in mathematics. Previous Oxford Presidents have included Peter Neumann, Marcus du Sautoy, David Acheson, Margaret Raynor, Michael Atiyah, Charles Coulson, Ida Busbridge and G. H. Hardy.

You can watch a selection of Vicky's talks and lectures here

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James Maynard awarded a New Horizons Prize for Early-Career Achievements in Mathematics

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Oxford Mathematician James Maynard has been awarded a 2023 New Horizons Prize for Early-Career Achievements in Mathematics in recognition of his multiple contributions to analytic number theory, and in particular to the distribution of prime numbers. 

James, who recently won the Fields Medal for his work, is recognised as one of the leading figures in the field of number theory. Much of his career has focused on the study of general questions on the distribution of prime numbers and his achievements include settling a long-standing conjecture of Paul Erdős on large gaps between primes and showing the existence of infinitely many primes missing any given digit (for example, 7).

More recently, in joint work with D. Koukoulopoulos he settled the Duffin-Schaeffer conjecture and dramatically improved upon the work of Schmidt concerning simultaneous approximation by rationals with square denominator. Most recently, he published a monumental series of works on the distribution of primes in residue classes which goes beyond what follows from the Generalised Riemann Hypothesis.

James Maynard did his undergraduate studies at Queens' College, Cambridge before moving to Oxford to do a DPhil under the supervision of Roger Heath-Brown where he has spent much of his career to date. He is now a Professor of Number Theory in Oxford and a Supernumerary Fellow at St John's College.

The New Horizons Prize is part of the Breakthrough Prizesthe world’s largest science awards founded by Sergey Brin, Priscilla Chan and Mark Zuckerberg, Julia and Yuri Milner, and Anne Wojcicki. The prizes recognise the top scientists in the fields of Life Sciences, Fundamental Physics, and Mathematics.

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Oxford Mathematics Public Lecture: A mathematical journey through scales - Martin Hairer

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The tiny world of particles and atoms and the gigantic world of the entire universe are separated by about forty orders of magnitude. As we move from one to the other, the laws of nature can behave in drastically different ways, sometimes obeying quantum physics, general relativity, or Newton’s classical mechanics, not to mention other intermediate theories.

Understanding the transformations that take place from one scale to another is one of the great classical questions in mathematics and theoretical physics, one that still hasn't been fully resolved. In this lecture, we will explore how these questions still inform and motivate interesting problems in probability theory and why so-called toy models, despite their superficially playful character, can sometimes lead to certain quantitative predictions.

Professor Martin Hairer is Professor of Pure Mathematics at Imperial College London. He was awarded the Fields Medal in 2014.

Please email @email to register.

The lecture will be available on our Oxford Mathematics YouTube Channel on 22 September at 5 pm.

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

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Roger Heath-Brown awarded the Sylvester Medal

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Oxford Mathematician Roger Heath-Brown has been awarded the Sylvester Medal by the Royal Society "for his many important contributions to the study of prime numbers and solutions to equations in integers". The Sylvester Medal is awarded annually by the Royal Society for an outstanding researcher in the field of mathematics. The award was created in memory of the mathematician James Joseph Sylvester who was Savilian Professor of Geometry at the University of Oxford in the 1880s.

Roger Heath-Brown is one of the foremost analytic number theorists of his generation. His important works on prime numbers and related topics include, among many others:

- "Heath-Brown's identity", an important way of decomposing the primes into multilinear pieces, used in many other works such as Zhang's work on bounded gaps between primes

- There are infinitely many primes of the form x^3 + 2y^3 (currently the sparsest natural sequence where one can find primes)

- if a is coprime to q, there is always a prime a (mod q) of size < q to the power 5.5

- at least one of 2,3,5 is a primitive root modulo infinitely many primes.

His contributions to solving equations in integers and rationals include, for instance:

- every nonsingular cubic form in 10 variables has a rational point (and 10 is best possible)

- every cubic form in 14 variables has a rational point

- development of "the determinant method"

- breakthrough quantitative results on the number of rational points up to a given height

Roger Heath-Brown was educated at Cambridge (a student of Alan Baker) and moved to Oxford in 1979. He was made FRS in 1993, and was twice a speaker at the International Congress of Mathematicians. He remained at Oxford throughout his career, first at Magdalen College and then, upon being promoted to a personal statutory professorship in 1999, at Worcester College. He retired in 2016. Among his many graduate students was James Maynard, who was awarded the Fields Medal in 2022.

You can watch an interview with Roger by Ben Green on occasion of his retirement (a loose term for a mathematician) .

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