News

No two subjects in the sciences are presented as being more different than mathematics and biology, so this is a very fair question to ask, especially as here, "mathematics" does not include statistics, while "biology" includes physiology, medicine etc. This talk will illustrate how mathematics has had a profound impact in biology.

In this Oxford Mathematics Public Lecture, Philip Maini will give examples including Alan Turing's groundbreaking work on biological pattern formation (which Philip has actually applied to football shirt patterns), Alan Hodgkin and Andrew Huxley's Nobel Prize winning explanation for neuronal signalling, and potentially new therapies for certain cancers.

Philip Maini is Professor of Mathematical Biology and Director of the Wolfson Centre for Mathematical Biology in Oxford.

Wednesday November 11th, 2026, Mathematical Institute, Oxford

Please email @email to register to attend in person.

The lecture will be broadcast on the Oxford Mathematics YouTube Channel on Wednesday 02 December at 5-6 pm and any time after (no need to register for the online version).

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

Oxford Mathematician Kaibo Hu 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.

Kaibo receives the prize for his work on numerical analysis, structure-preserving discretisation, Finite Element Exterior Calculus, discrete geometry and discrete topology, computational topological hydrodynamics, and numerical relativity.

Kaibo Hu is a Senior Research Fellow and Associate Professor at the Mathematical Institute, University of Oxford, and a Royal Society University Research Fellow. His research concerns structure-preserving numerical methods and the connections between computation, geometry and topology. He works on finite element exterior calculus and finite element tensor calculus, with applications to magnetohydrodynamics, continuum mechanics, numerical relativity and geometric PDEs.

He obtained his PhD from Peking University in 2017 and subsequently held positions at the Universities of Oslo, Minnesota, Oxford and Edinburgh. At Edinburgh, he was a Reader before returning to Oxford in 2025. He leads the ERC Starting Grant project GeoFEM (Geometric Finite Element Methods). In 2026, he was invited to give the Nachdiplom lectures at ETH Zurich. He received the SIAM Computational Science and Engineering Early Career Prize in 2023 and the Stephen Smale Prize in 2026.

Each of the 30 Prize Winners receives £100,000 which can be used for any purpose to advance their research.

Much has been written about the Riemann hypothesis, which many consider to be the most important unsolved problem in mathematics today. It concerns the zeros of the Riemann zeta function, which Riemann introduced in his famous 8-page paper from 1859. This talk aims to explain the motivation behind his paper, which only incidentally mentioned the Riemann hypothesis. This story has many sequels. 

David E. Rowe is Professor Emeritus for History of Mathematics and Natural Sciences at Johannes Gutenberg University in Mainz.

Wednesday 28 October, 5 pm, Andrew Wiles Building, Oxford

The University of Oxford has welcomed the first cohort of DPhil students to Oxford × QRT Labs, part of a long-term research initiative between Qube Research & Technologies (QRT) and the universities of Oxford, Cambridge and Imperial College London.

Four DPhil students make up Oxford × QRT Labs’ first cohort, with one researcher based in each of the Mathematical Institute, Department of Statistics, Department of Engineering Science and Department of Computer Science.

The launch also marks the appointment of Professor Blanka Horvath as Director of Oxford × QRT Labs.

Oxford × QRT Labs forms part of a wider research network bringing together early-career researchers, academics and QRT’s research and technology community. The initiative is designed to support fundamental research while creating opportunities for researchers to exchange ideas across disciplines and institutions and to engage with industry and the wider scientific and technological community.

Across Oxford, Cambridge and Imperial, the first QRT Labs cohort comprises 13 early-career researchers working across mathematics, statistics, computer science and engineering. Their research spans areas including AI and its mathematical foundations, intelligent systems, decision-making under uncertainty, scientific and high-performance computing, optimisation, and advanced mathematical and statistical modelling.

Researchers will also have opportunities to connect across the wider QRT Labs network through seminars, events and an annual conference, encouraging exchange between disciplines, institutions and QRT’s research community.

In the last few years, large language models (LLMs) have undergone significant development: in their capabilities, in the variety of their applications, and in their prevalence in our world. They have evolved from relatively fluent text generators to proficient reasoning models with which most people interact on a daily basis.

While this progress has, in part, been driven by scale, data, and compute as well as careful engineering, an additional contributor to this development has been an improved theoretical understanding of the transformer architecture on which these models are based. In particular, the self-attention mechanism distinguishes the transformer from machine learning models which came before it. The mathematical structure of this component has proven considerably richer than might be expected from its relatively simple formulation. There is, therefore, an ongoing programme which seeks to provide insight into the underlying behaviour of LLMs by establishing a firm theoretical understanding of the transformer.

On August 21, 2026, Oxford Mathematics hosted the second edition of the “Workshop on the Mathematics of Transformers”, following a first edition at DESY in Hamburg in September 2025. The workshop aimed to bring together researchers in multi-agent dynamics, optimal transport, and partial differential equations, with the common objective to improve the theoretical understanding of the transformer and the underlying self-attention mechanism.

Close to 40 participants, coming from different institutions, countries and disciplines, gathered to discuss open questions and results that we hope will shape a fundamental understanding of LLMs.

Programme

The workshop featured six invited talks given by,

• Samira Kabri (Helmholtz Imaging, DESY) on Anisotropic interaction in self-attention layers,
• Thomas Jacob Maranzatto (University of Maryland) and Jan Peszek (University of Warsaw) on Diverse dynamical behaviors in deep linear transformers,
• Domènec Ruiz-Balet (University of Barcelona) on Hardmax attention dynamics,
• Albert Alcalde (University of Erlangen–Nuremberg) on Quantifying low-temperature concentration in mean-field transformers,
• Edoardo Calvello (California Institute of Technology) on Transformers for operator learning on probability measures: from theory to scientific workflows,
• William Gibson (University of Oxford) on Uniform scaling limits in AdamW-trained transformers.

Most of the talks were concerned with the dynamics of self-attention at inference. The starting point in this line of research is a setting where tokens converge to consensus, a small number of clusters, or concentrate on lower-dimensional spaces. Several of the results presented investigated this picture in different regimes. Allowing the interaction between tokens to be anisotropic changes the stationary states of the dynamics. Working outside the gradient flow framework, on a lower-dimensional invariant manifold, makes it possible to observe cycling and bifurcations as well as clustering, and connects the dynamics to the Kuramoto model. The hardmax limit of the attention mechanism leads to a different class of PDE problems. A further result showed that at low temperature the token distribution concentrates quickly into a metastable state, and that the metastability of this state depends on a hyperparameter.

Two talks went beyond this setting. One used the description of attention as a map between probability measures as a design principle rather than as a tool for analysis, and applied it to nonlinear data assimilation, where it improved on ensemble Kalman baselines. The second considered the large-depth limit of transformers trained with AdamW, and established convergence of the hidden state dynamics to a forward-backward system of ODEs, with bounds that do not depend on the number of tokens.

Outlook

The response to this workshop, and to its predecessor, has been overwhelmingly positive. What came out of the day was a sharper sense of the open problems: the discussions brought them into clearer focus and left participants with a better sense of which questions are worth pursuing and which tools are likely to reach them. Several exchanges pointed towards new collaborations across institutions. Given the extent of the engagement and curiosity for the subject, we were very happy to find that a third edition of the workshop was a late-night topic of discussion.

Thanks

The workshop was jointly organised by José A. Carrillo, Daniel Kelly, Konstantin Riedl (University of Oxford) and Tim Roith (Technical University of Munich), and kindly supported by G-Research and the Advanced Grant Nonlocal-CPD: “Nonlocal PDEs for Complex Particle Dynamics: Phase Transitions, Patterns and Synchronization” of the European Research Council Executive Agency (ERC).

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  postgraduate foundation that offers full funding and multi-year support for outstanding UK students to complete STEM PhDs and MSc courses at leading UK research universities. Mathematics at Oxford is a core component of Martingale.

Martingale Scholars will receive funding for the full cost of a PhD or MSc 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.

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.

Find out more about the scholarships, how to apply and the work and aspirations of the Martingale Foundation whose generosity enables these scholarships to be awarded.

Below is a video of our first cohort of Martingale Scholars talking about their experience.

Count me in: how mathematics explains music - Sarah Hart

Wednesday 12 August 2026, 5.00-6.00 p.m., Lecture Theatre 1, Mathematical Institute, Oxford

Oxford Mathematician Graeme Segal has been awarded the Chern Medal in recognition of an outstanding lifelong achievement at the highest level in the field of mathematics. The medal is named in honour of the Chinese-born American mathematician Shiing-Shen Chern and was announced today at the International Congress of Mathematics (ICM) in Philadelphia, USA.

Graeme Segal, for whom Shiing-Shen Chern was a major inspiration, is a geometer and topologist whose profound contributions at different stages of his career have enriched and advanced both mathematics and physics. His early work established foundational results in algebraic topology (particularly homotopy theory) that had a major influence on the subsequent development of that subject. Later, his powerful and elegant work on quantum field theory and string theory was central to the forging of new links between pure mathematics and theoretical physics, elucidating "the role of the concept of space in fundamental physics" as Graeme himself described it.

Graeme was born in Australia and did his undergraduate studies in Sydney, before coming to England to study in Cambridge and Oxford. He was Lowndean Professor of Astronomy and Geometry, and Fellow of St John’s College, Cambridge from 1990 to 1999 and Senior Research Fellow, All Souls College, Oxford from 1999 to 2009 where he is now an Emeritus Fellow. He is a Fellow of the Royal Society and a former President of the London Mathematical Society and was awarded its Polya Prize in 1991. In 2010 he received the Royal Society’s Sylvester Medal for mathematical research.