Conference programme and slides now available

Timothy Abrahams on 19 August, 2026

A list of talk abstracts and slides from the Mathematical Foundations of AI Conference can be found below.

Erik Bekkers
From Spinoza to Equivariance: Geometry as the Shared Structure of Mind and Matter
What is intelligence, and how does mind relate to matter? I want to start where Spinoza did, in 17th-century Amsterdam. He treated metaphysics with the rigor of geometry, and concluded that mind and matter are two attributes of one and the same substance, not two separate substances. I think that starting point is still the right one.

We never reach reality directly, only through representation, so we cannot leave the observer out of our account of the world, and matter as we know it is already a description shaped by mind. If mind and matter are two aspects of one reality, they are governed by the same laws, and since our best account of those laws is geometric, geometry is the structure they share. If our models are to represent reality faithfully, their internal organization should respect that geometry, which is why equivariance is not optional. In the talk I follow this line from Klein’s Erlangen Programme through geometric deep learning, and show that equivariance now comes at no extra cost, that scale does not replace it, and that the current frontier is to carry geometric structure into the latent space: world models, generation on manifolds, and novel view synthesis. I call this vision Ideal Machine Intelligence.

Rebekka Burkholz
Towards AI That Is Smart, Sparse and Social
Deep learning continues to achieve impressive breakthroughs across disciplines but relies on increasingly large neural network models that are trained on massive data sets. Their development inflicts costs that are only affordable by a few labs and prevent global participation in the creation of related technologies. But does it really have to be like this? We will identify some of the major challenges of deep learning at small scales and present solution strategies pertaining to the design of sparse training algorithms and problem specific neural network design. As examples, we will discuss NeuralODE models of gene regulatory dynamics and agentic networks, which hold the promise to overcome a fundamental trade-off between model specialization and trainability.

Kevin Buzzard
On autoformalization
Formalization is the art of translating mathematics from a human language such as English into a formal language such as Lean. Autoformalization is when an AI tool does it for you. I’ll speak about what’s been happening recently in the area.

Coralia Cartis
Towards understanding feature learning: low-rank functions and data properties
Low-rank or multi-index functions appear in both optimization and machine learning, displaying structure simplicity that allows dimensionality reduction and captures the important directions of variation of the landscape. This allows efficient optimization and learning or generalisation. We will discuss some relatively new occurrences of low rank objectives, such as when considering trained nets as functions of the training data, and the implications of this on robustness of training and the learning of important features. Time permitting, we will also discuss training data recovery algorithms, where we show both theoretically and numerically that given final and initial parameters of the trained network, as well as access to network gradients, and provided the network is sufficiently (but finitely) wide, we can recover training data samples to desired accuracy efficiently, by using only a subset of the parameters and low-rank properties of the data. Throughout our work, we will discover interesting connections between the data and the parameters of deep neural networks.

Oliver Clarke
Hierarchical embeddings and phylogenetic ranks of graphs
The phylogenetic rank of a finite metric space as introduced by Pachter and Sturmfels is the minimal number of metric trees needed to embed it isometrically. Here, the product of metric trees is endowed with the supremum norm. Intuitively the phylogenetic rank gives us a discretely measure of how far away a space is from being a tree. In this talk I will show how the phylogenetic rank is subadditive under certain constructions. I will also explain recent work where we develop both a greedy and an exact algorithm for computing phylogenetic ranks of metric spaces arising from graphs. Using our algorithms, we construct a database of phylogenetic ranks which includes all graphs on at most 7 vertices. In particular, we exhibit examples disproving: the phylogenetic rank is a hereditary property; bounded by half the number of points of the space; and a generalised 4-point conjecture by Pachter and Sturmfels. My work is joint with F. Ashworth, J. Giansiracusa, J. Jones, J. Quias-Acaves, Y. Ren.

Francesco Fabiano
Enhanced Decision-Making for AI Reasoning
This talk focuses on how AI decision-making can be enhanced through both existing logical or symbolic approaches and neural, experience-based methods. I present decision-making as the core process that connects reasoning, learning, memory, and action selection. The talk shows how decision-making can be improved in multiple directions: through robust and game-theoretic methods for uncertain environments, through cognitive architectures inspired by fast and slow thinking, and through neural approaches such as GNN-enhanced epistemic reasoning. Across these directions, the key idea is that better AI reasoning often comes from using the right heuristics and relaxations: mechanisms that reduce computational complexity, guide search, and allow agents to make effective decisions even when full reasoning is too expensive or uncertain.

Holly Francois
AI in Online Safety Regulation: Use Cases and Considerations
The rapid adoption of generative artificial intelligence is transforming the design and operation of online services, creating both new opportunities and emerging challenges for online safety regulation. This presentation explores the role of AI within the UK’s Online Safety Act framework and examines how regulators can address the risks and benefits associated with increasingly autonomous and generative systems. Drawing on experience from Ofcom’s Online Safety Technology team, the talk considers how AI is reshaping key safety-critical functions, with a focus on real world use cases and potential emerging risks. Particular attention is given to AI-driven recommender systems, the challenges of explainability and oversight in automated moderation, and the growing use of AI chatbots as companions, including potential impacts on children and vulnerable users. The discussion concludes by identifying priority research areas that can support evidence-based regulation and help ensure that advances in AI contribute to a safer online environment while preserving fundamental rights and freedoms.

Peter Grindrod
Next Generation and Generation After Next AI; mathematical underpinnings of creative disruption and fundamental understanding for responsible use
Mathematics will be both the innovator and the disruptor in the next phase of AI. It will move us beyond systems that merely correlate toward systems that reason, adapt, and justify their actions within known limits. It will help us replace blind trust with warranted confidence. And it will enable forms of creativity, not just in generating content, but in solving problems that are rigorous, accountable, and genuinely new. If we want AI that society can rely on, mathematics must be at its core. That is not a constraint on progress. It is the condition that makes progress sustainable.

Maz Hardey
The Liminal Place: AI, Math, and Human Variance in V Movements
Modern computational optimisation operates on a quiet, unsparing logic: treating friction, uncertainty, and human variance as structural defects to be engineered away. As machine learning models convert the warmth of human language, art, and reasoning into high-dimensional vector spaces, they succeed in minimising mathematical loss – yet in smoothing that terrain, they risk erasing the quiet interval where genuine understanding actually takes root. Drawing on her research across digital platforms, family systems, and computing cultures, Prof Mariann Hardey (Prof Maz) explores how algorithmic homeostasis penalises the atypical mind, swapping the spiky reality of real thinking for a safe, synthetic average. Moving through visual art, higher education’s ‘cringe deficit,’ William Thurston’s human-centred proofs, and neurodivergent variance, this talk challenges computer scientists, business leaders and mathematicians to reconsider the role of friction in intelligent systems. Rather than building high-speed off-ramps for cognitive and emotional discomfort, Hardey offers a constructive call for liminal-preserving architectures: computational systems designed to hold the pause, honour human variance, and safeguard the quiet space where original thought takes breath.

Kathryn Hess
Ring scores: quantifying circularity in data
I will give an overview of the theory of ring scores, which are numerical invariants of compact metric spaces that measure the prominence of circular structure, enabling a “circularity analysis” analogous to classical cluster analysis. Ring scores satisfy four axioms that together encode how closely a metric space resembles the standard circle equipped with its arc-length metric. I will explain how to characterize ring scores that factor through the degree-$1$ persistence diagram of the Vietoris-Rips filtration and sketch a stability theorem for the lifespan ring scores associated to it. To conclude I will outline an application of ring scores as a screening statistic for the detection of cyclic cell processes in single-cell data. (Joint work with Markus Youssef)

Stefanie Jegelka
Neural parameter symmetries: Learning on LoRAs, breaking symmetries and the effect of data
Parameter symmetries within neural networks govern important properties, including the optimization landscape and training behavior and model merging. They are also an important consideration when aiming to make predictions about neural networks from their weights, i.e., in the emerging area of weight space learning. In this talk, we will discuss aspects of neural parameter symmetries via illustrative examples. First, we build models to predict the performance of LoRA (low-rank adaptation) finetunes of generative models much faster than running the actual evaluation. Here, neural networks are inputs for our prediction, and due to the cost of learning on neural weights, taking into account symmetries can be particularly beneficial here. Second, we study the effect and behavior of symmetries within neural networks. To do so, we devise methods for removing such symmetries, as a tool for studying their effect. While doing so, we observe that the geometry of the data, although neglected by many works on symmetries and merging, plays an important role, too.

Roland Kwitt
Scaling-Up Persistent Homology Computation
This talk examines the computational challenges of scaling persistent homology for 3D point-cloud data. Scaling is considered along two complementary axes: increasing the number of points within each point cloud and processing large collections of point clouds in practical machine-learning pipelines. I will discuss applications in which the computational and memory requirements of current persistent-homology methods – and the subsequent vectorization of persistence diagrams – have so far limited their large-scale use. Finally, I will present some preliminary developments in learning directly from the underlying filtered simplicial complexes, using representations that capture topological and spectral information while bypassing explicit persistence reduction and diagram vectorization.

Richard Lane
Classifier Probability Calibration
Probabilities produced by AI models often do not reflect their true accuracy, being under- or over-confident in their predictions. If a model is 80% sure of an outcome, is it correct 80% of the time? Understanding calibration is important for assurance in safety or business-critical contexts and builds user trust in models. Probability calibration metrics measure the discrepancy between confidence and accuracy. We recently published a comprehensive review of such metrics, grouping them into four main families: point-based, bin-based, kernel or curve-based, and cumulative. This talk provides an overview of the metrics and how they can be used in practice.

Darrick Lee
The geometry of cochains on sampled point clouds
Manifold learning often begins by approximating an unknown continuum geometry with a graph, whose Laplacian can converge to the Laplace–Beltrami operator. However, a manifold also carries higher-order structure: differential forms, cohomology, and Hodge Laplacians. In this talk, we describe a framework for approximating this structure using simplicial complexes built from point-cloud data. We discuss the discretization of differential forms as simplicial cochains, which we equip with inner products based only on ambient distances. We provide probabilistic convergence results of these discrete constructions to their continuum analogues and consider their consequences for the discrete Hodge Laplacian. Based on joint work with Kelly Maggs.

Eng-Jon Ong
From Memorization to Simplification: A Three-Phase Explanation for Grokking
This talk concerns the deep learning phenomenon of “grokking,” where overparameterized neural networks exhibit delayed generalization, with accuracy on unseen data improving long after perfect training accuracy has been achieved. Existing work considers grokking through the lenses of the transition from lazy to rich training dynamics, late-stage neural collapse, and the information bottleneck principle. However, the precise mechanical evolution of internal hidden representations during this delay remains an open question. We show empirically, alongside a mathematical framework, how the learning process unfolds across three distinct phases: Phase 1) memorization, Phase 2) feature compression, and Phase 3) model simplification, with Grokking occuring in the last 2 phases. We demonstrate how Phase 2 is governed by an anisotropic spectral compression: the cross-entropy loss acts as a soft margin constraint that shields task-relevant weight matrix singular vectors, while weight decay compresses out the uninformative directions. Once this passive compression reaches its limit, Phase 3 begins. In this final phase, the weight vectors actively rotate, causing a collapse in the stable rank of each hidden layer. This alignment effectively produces a simplified model that exhibits improved generalization and robustness to both unseen and adversarial examples.

Yue Ren
Optimization in Polydisc Spaces: A Non-Archimedean Framework for Hierarchical Data
Hierarchical data is ubiquitous in many applications, whether it be inherent in the problem (phylogenetics, genomics, etc) or artificially introduced by humans (language processing, computer vision, etc). Prime example are international logistic networks, where locations are clustered first by city, then county, then country, and finally continent. An intrinsic characteristic of hierarchical data is the fact that distances do not add up. Regardless how far you move within a city, it will never get you out of the county. This property is called the non-Archimedean property. It is the reason why hierarchical structures are difficult to capture over the real numbers, and why their analysis is challenging.

Existing workarounds include working in hyperbolic space or working in very high dimensions (as seen in large language models). A natural approach is using non-Archimedean fields such as the p-adic numbers. While these fields are indispensable in number theory, where their hierarchical structure allows the study of polynomial equations prime by prime, optimisation in non-Archimedean spaces remains challenging: their totally disconnected topology prohibits the use of many standard optimisation techniques.
In this talk, we propose a new framework for analyzing hierarchical data in the form of so-called polydisc spaces over non-archimedean fields. Inspired by the theory of Berkovich geometry, we show these polydisc spaces retain the hierarchical structure of their non-archimedean field while acquiring many desirable geometric features absent from it. As such, they are capable of both serving as a representation space for hierarchical data as well as a domain amenable to standard optimisation algorithms.

Moreover, we present NonArchimedeanMachineLearning.jl, a new Julia library for optimisation in polydisc spaces. This is joint work with Paul Lezeau, Yiannis Fam, and Anthea Monod.

Tatiana Shavrina
AI Agents changing Scientific Discovery
AI research agents are rapidly transforming scientific discovery by automating complex research workflows. This talk surveys recent advances in frontier agentic systems, LLM-based research assistants, and evaluation benchmarks. We will examine agent performance across the scientific lifecycle—from hypothesis generation to experimentation and refinement—and discuss the remaining challenges toward truly autonomous scientific discovery.

Suvrit Sra
Tight generalization bounds in Inverse Optimization
Inverse optimization (IO) seeks to infer the parameters of a decision-maker’s objective from observed context–action data. We study noiseless IO, where demonstrations are generated by a ground-truth objective. We provide a high-probability O(d/T) generalization bound for the induced action set, where d is the number of unknown parameters and T is the size of the training dataset. We strengthen these guarantees under additional conditions that ensure uniqueness of the chosen action, bringing our IO guarantees in line with best-arm identification results in the bandit literature.

We further show that the O(d/T) rate is tight over all consistent estimators considered here, and extend the result to both instantaneous and cumulative regret. Notably, the resulting regret lower bound matches the corresponding upper bounds in the adversarial setting, indicating that the stochastic IO setting is effectively adversarial for the class of estimators studied here. Finally, we propose a parameter-free algorithm with lower per-iteration complexity than generic solvers. Experiments validate the predicted rates and illustrate the tightness of our bounds.

Marika Taylor
Physics inspired learning: geometry and symmetries
Physics-inspired neural networks (PINNs) can be thought of as models whose design and training incorporates physical principles such as symmetry and locality, as well as dynamical equations of motion. For example, rotation equivariant networks can be more efficient in classification of 3d images, while PINNs used for fluid dynamics problems penalise deviations from solving the fluid equations of motion. In this talk we will explore how underlying geometrical and symmetry structure can be built into networks, with a particular focus on networks used for analysis of quantum data.

Qiquan Wang
The Shape of Adversarial Influence: Characterising LLM Latent Spaces with Persistent Homology
Existing interpretability methods for large language models (LLMs) typically focus on linear directions or isolated features, which can miss the high-dimensional and nonlinear geometry of internal representations. In this talk, persistent homology is used to characterise the geometry of LLM latent spaces and to study how these representations are reshaped under adversarial inputs. Across multiple models (3.8B–70B parameters) and different attack settings, including indirect prompt injection and backdoor fine-tuning, a consistent phenomenon of topological compression is observed. Adversarial inputs induce a simplification of the latent space, where varied small-scale structure collapses into fewer dominant large-scale features. This signature is found to be architecture-agnostic, emerges early in the network, and remains highly discriminative across layers. By quantifying the shape of activation point clouds, this perspective reveals geometric structure in representational change that complements existing linear interpretability approaches.

George Williamson
From Possible to Proven: is the Erlangen Programme for AI a National Infrastructure programme?
Felix Klein’s Erlangen Programme didn’t just tidy up geometry: it gave mathematicians a shared language for understanding which properties were preserved across different geometrical transformations, and which were not. Modern AI still lacks an equivalent framework. We can build systems that work, often remarkably well, but we struggle to characterise in advance the conditions under which their behaviour will remain predictable, robust, and reliable. AI possesses many partial theories of generalisation and failure, but no unifying framework that plays a comparable role. That gap is no longer a purely academic concern. As AI becomes embedded in critical infrastructure, defence, and public services, uncertainty about its failure modes becomes a matter of national resilience rather than scientific tidiness. This talk argues, from inside the UK’s national institute for data science and AI, that the mathematical foundations agenda represented by this hub is not simply upstream of deployment, but must be intimately connected to it. I’ll reflect on what it would take to move from mathematically interesting to institutionally trusted, and ask whether AI needs its own analogue of the Erlangen Programme before it can be relied upon as national infrastructure.

Arne Wolf
Breaking Symmetry Bottlenecks in GNN Readouts
Graph neural networks (GNNs) are widely used for learning on structured data, yet their ability to distinguish non-isomorphic graphs is fundamentally limited. These limitations are typically attributed to message passing. This talk reveals an independent bottleneck at the readout stage. We introduce fundamental notions of finite-dimensional representation theory to prove that all linear permutation-invariant readouts, such as sum and mean pooling, inevitably project node embeddings onto a fixed subspace. This erases all non-trivial symmetry-aware components, regardless of how powerful the encoder is. To study and mitigate this bottleneck, we introduce projector-based invariant readouts that decompose node representations into symmetry-aware channels and summarize them with nonlinear invariant statistics. Finally, we demonstrate how modifying only the readout enables fixed encoders to separate WL-hard graph pairs and improves performance on symmetry-sensitive tasks.

Ka Man (Ambrose) Yim
Testing for Spatial Randomness with a Topological Stein Statistic
We propose a novel statistic for testing whether a given point cloud is completely spatially random. Usual spatial randomness tests rely on comparing test statistics (such as nearest neighbour distance distributions) of a given point cloud with those in the completely spatially random case. Our Stein Statistic enhances a test statistic by baking in properties of a completely spatially random model in the statistic itself. This is accomplished using a Stein operator for the Poisson point process (a model for completely spatially random point clouds). By augmenting topological test statistics with a Stein operator, we demonstrate its empirical effectiveness on synthetic point clouds and show theoretical asymptotic convergence results of this statistic. This talk features joint work with Gesine Reinert and Omer

Academy publishes new Whitehall AI primer

Timothy Abrahams on 22 July, 2026

Members of the Erlangen AI Hub alongside colleagues from the Prob_AI Research Hub and INFORMED-AI Hub have made contributions to An excellent initiative from the Academy for the Mathematical Sciences, highlighting the critical role that mathematics plays in the structures of AI. The primer is directed particularly at civil servants grappling with the subject.

The primer ‘Mathematics in the age of AI’ provides an accessible introduction to many key topics shaping the future of AI, and can support analysts, policymakers, and decision-makers in government. In the words of Nigel Campbell, the Academy for the Mathematical Sciences Vice President and former Senior Civil Servant: 

 “As AI becomes increasingly important across the economy and public services, the need for strong mathematical capability will only grow. This primer makes clear that sustained investment in the mathematical sciences is not simply an investment in research, but an investment in the capabilities needed to realise the benefits of AI responsibly and effectively.”

As we noted on social media at publication date, strong mathematical foundations are indeed essential for developing robust, trustworthy systems. This primer picks out some of the key mathematical principles underpinning modern AI. It also shows how the mathematical sciences underpin modern AI and will determine the form and success of development in the future. The document also shows how any attempt to develop new algorithms and improve reliability will give the mathematical sciences a central role in AI progress. It explains how a strong mathematical ecosystem is essential to the UK’s
capacity to develop the next generation of AI and shows how our field will be essential in evaluating and deploying technologies in a responsible efficacious manner. It also makes the important point that only with sustained investment in education and research can the mathematical sciences achieve this goal.

It also showcases real life applications and sketches out the challenges ahead and is therefore a must read.

DOWNLOAD HERE

UK AI Hubs launch national challenge for early career researchers

Timothy Abrahams on 3 June, 2026

The Erlangen AI Hub is taking part in an exciting new initiative, the AI Hubs National Public Engagement Challenge with Expressions of Interests needed this month (June). The competition offers PhD students and Postdoctoral Researchers within the UKRI AI community a chance to present their work in a compelling three-minute video designed for a public audience, and to showcase the depth and diversity of UK AI research on a national stage.

For early career researchers looking to strengthen their communication profile and raise the visibility of their work, this is an excellent opportunity. Participants will:

  • Build valuable public engagement skills essential for grant applications and careers.
  • Receive expert training on how to translate complex research into engaging stories.
  • Connect with peers across the UK AI Hubs, expanding their network.
  • Gain visibility across the UK AI ecosystem.
  • Compete for a spot in the national final, where the top five videos will be presented at the UKAIRS 2026 conference dinner in November, before an audience of policymakers, funders, industry leaders and researchers.
  • Potentially take home the title of Overall Winner.

The challenge is open to researchers connected to a UK AI Hub through any of the following:

  • Postdoctoral researchers employed on a UKRI AI Research Hub
  • PhD students within a UKRI AI CDT or another Doctoral Training Programme aligned to AI research
  • PhD students or PDRAs within the research group of an AI Hub Co Investigator, Partner or Member

If you are connected to a UK AI Hub, this is your chance to get involved. Eligible researchers must submit an Expression of Interest by 12 June 2026 including:

  • Name
  • Role: PhD Student or Postdoctoral Research Associate
  • Name of CDT or AI Research Hub
  • A 300-word description of their research for a general audience
  • A 150-word statement on why they want to take part

Submit your Expression of Interest by email by 12 June 2026 to info@aichemy.ac.uk with the subject line: ‘AI Hubs: National Public Engagement Challenge’

Shortlisting will take place on 24 June 2026, with 20–30 researchers selected to progress. Selected researchers will attend an online training session on presenting to public audiences and structuring an effective three-minute pitch. The session will also offer opportunities to practise with peers from other Hubs. Participants will then create their own three-minute video, using one slide (animation permitted). The final criteria for judging will be confirmed beforehand. A panel of external reviewers, including EPSRC Project Officers, will select the five finalists. All videos will be shared online to highlight the breadth of AI research across the UK.

The five finalists will be invited to attend UKAIRS 2026 (to be held at John McIntyre Conference Centre, Edinburgh above) on 24–25 November and their videos will be showcased at the conference dinner. A judging panel external to the Hubs covering policy and communication specialists will select the overall winner. If you are an early career researcher associated with a UK AI Hub, don’t miss this chance to share your work, develop your skills, and connect with the wider AI community.

Start preparing your Expression of Interest and bring your research to life in three minutes!

Final speakers announced for conference

Timothy Abrahams on 28 May, 2026

A finalised list of speakers for the Mathematical Foundations of AI Conference 2026 has almost been arrived at. The experts we have already secured stand at the intersection of mathematics, machine learning, artificial intelligence, geometry and topology. From pioneers of geometric deep learning and graph neural networks to leading researchers in topology, optimisation, formal proof verification, and relational AI, the conference will showcase cutting-edge ideas shaping the future of intelligent systems.

A list of the major speakers is included below. By the very nature of their wide-ranging contributions the following biographies have been edited for brevity.

Erik Bekkers
Erik Bekkers is an associate professor in Geometric Deep Learning in the Machine Learning Lab of the University of Amsterdam. His work emanates from the belief that as nearly all data is rooted in our physical world it is thus inherently grounded in geometry and physics and representation learning should preserve this grounding. His current research focuses on developing generalizations and efficient implementations of group equivariant architectures. 

Michael Bronstein
The Erlangen AI Hub founder and co-director is a pioneer of geometric deep learning and graph neural networks. In addition, Michael Bronstein is DeepMind Professor of AI at the University of Oxford, Erlangen AI Hub Director and Founding Scientific Director of AI at AITHYRA. His work bridges academia and industry, shaping the future of non-Euclidean machine learning and AI innovation.

Rebekka Burkholz
Rebekka Burkholz is a tenured faculty member at the CISPA Helmholtz Center for Information Security, researching relational machine learning. Her main goal is to gain a theoretical understanding of deep learning from a complex network perspective and improve contemporary algorithms based on these insights. Her current applications focus on molecular biology. Before joining CISPA in 2021, she worked at the Biostatistics Department of the Harvard TH Chan School of Public Health.

Kevin Buzzard
Professor of Pure Mathematics at Imperial, Kevin Buzzard won the London Mathematical Society’s Whitehead Prize in 2002 and the Senior Berwick Prize in 2008. In 2017 he started formalizing mathematics and in 2022 he gave a plenary lecture at the International Congress of Mathematicians on the topic. He is currently leading a project to formalize a proof of Fermat’s Last Theorem and will speak at the conference on what autoformalization means with regard to artificial intelligence.

Coralia Cartis
Coralia Cartis is Professor of Numerical Optimization, University of Oxford, an internationally recognised mathematician whose research focuses on the theory, complexity and implementation of optimisation algorithms central to modern machine learning. A SIAM and EUROPT Fellow, she has made influential contributions to non-convex optimisation, derivative-free methods and large-scale computational mathematics. Cartis’s research bridges optimisation theory and AI applications, with expertise in numerical optimisation and machine learning algorithms.

Holly Francois
Holly Francois is Principal for Data Innovation (Machine Learning) at Ofcom, the UK’s communications regulator. She leads machine learning for online safety, combining AI research with regulatory practice. She has an extensive track record in international standards (3GPP, ITU-T and ETSI), and AI, with expertise spanning deep learning, transformers, speech recognition and generative AI.

Peter Grindrod
Peter Grindrod CBE is CEO of Astut Ltd, Professor of Mathematics at the University of Oxford and a leading applied mathematician whose work has shaped the development of mathematical approaches to data science and artificial intelligence in the United Kingdom. A founding director of the Alan Turing Institute and co-investigator of the Erlangen AI Hub, he has championed the view that future advances in AI depend on deeper mathematical understanding rather than scale alone. His research connects theoretical mathematics with industrial and societal applications

Mariann Hardey
Professor Hardey is a leading expert in Human-AI interaction, digital accessibility and equity. Her work, including her pivotal role as an Associate Director in the new Leverhulme Centre for Algorithmic Life, and her focus on the theme of Being Human is driven by a profound vision of technology that serves everyone. Inspired by the insight of HG Wells into a future shaped by innovation, her research focuses on harnessing the power of technology to empower individuals and communities. Professor Hardey is also part of Advanced Research Computing (ARC) at Durham University.

Kathryn Hess
Kathryn Hess is a leading mathematician known for her work in homotopy theory, category theory, and algebraic topology, as well as for applying topology to neuroscience, cancer biology, and materials science. Professor at École Polytechnique Fédérale de Lausanne, she is also a member of the Swiss Academy of Engineering Sciences, a Fellow of the American Mathematical Society and the Association for Women in Mathematics.

Stefanie Jegelka
Humboldt Professor at TU Munich and a Visiting Associate Professor at MIT EECS , Stefanie Jagielka’s research investigates the combinatorial, geometric, and algebraic foundations of machine learning. This includes learning with discrete objects, such as graphs or sets; learning with symmetries; discrete probability; learning with limited supervision, and the interplay of discrete and continuous optimization. She was a postdoc at UC Berkeley and obtained her PhD from ETH Zurich and the Max Planck Institute for Intelligent Systems.

Roland Kwitt
Professor of Machine Learning within the Department of Artificial Intelligence and Human Interfaces (AIHI) at the University of Salzburg (PLUS), Roland Kwitt is also currently deputy head there. Prior to that, he was part of the medical imaging and computer vision group at Kitware Inc., North Carolina, USA. His research spans multiple areas, but mostly focusses on theoretical and practical aspects of learning methods that allow the leverage and control structural characteristics of data. He is also a member of the ELLIS society.

Richard Lane
Richard is a Principal Data Scientist and Chartered Engineer at QinetiQ with 25 years’ experience in applying statistical and signal processing techniques to defence and security problems. Richard was awarded the John Benjamin Memorial Prize for his work on maritime anomaly detection and threat assessment, culminating in a demo to representatives from the Royal Navy, UK Border Agency and the Police. Richard has written over 130 journal and conference papers, patents and technical reports and was awarded a QinetiQ Fellowship in recognition of this and his project delivery record.

Yue Ren
Associate Professor, Durham University and UKRI Future Leaders Fellow, Yue Ren is a mathematician whose research connects algebraic geometry, tropical geometry and machine learning. He is a leading developer of mathematical software systems including Polymake, Singular, and OSCAR, and explores how geometric and algebraic structures can illuminate the behaviour of neural networks and learning algorithms. His work brings rigorous mathematical tools to problems in AI, polynomial system solving and scientific computing, with expertise in tropical geometry and geometric machine learning.

Suvrit Sra
Suvrit Sra is Career Development Associate Professor of EECS MIT and Professor for Resource Aware Machine Learning at TU Munich. A main component of his research on the mathematics of AI is optimization for machine learning, especially non-convex optimization including non-Euclidean and geometric optimization. Other key topics of interest include: discrete probability, theory of deep learning, theory of sampling, convex geometry, polynomials, combinatorics, etc.

Marika Taylor
Marika Taylor is Head of the College of Engineering and Physical Sciences and Pro Vice Chanceller at the University of Birmingham. She is also Professor of Theoretical Physics whose recent work extends into the mathematical foundations of artificial intelligence. Originally renowned for contributions to string theory, holography and geometry, she has increasingly focused on geometric AI and mathematically principled approaches to machine learning. As a Fellow of the Alan Turing Institute, she promotes interdisciplinary research linking advanced mathematics, physics and data science.

George Williamson
George Williamson is CEO of The Alan Turing Institute. Prior to this, from 2021, George was CEO of HMGCC (His Majesty’s Government Communications Centre), leading the organisation’s work to create tools and technologies for the national security community. George previously held a series of senior roles within the Foreign, Commonwealth and Development Office (FCDO), most recently as a Director General in Technology, serving in the UK’s diplomatic service for over 20 years, with roles in both the UK and overseas. George holds a DPhil from Oxford, was a Kennedy Memorial Scholar at Harvard University, and was Lecturer in Ancient History at Corpus Christi College, Oxford.

Register now to reserve your place at the conference and follow us for further speaker announcements over the coming weeks.

Erlangen AI Hub Industry Day: Connecting Academia and Industry

erlangenaihub on 28 April, 2026

On Tuesday 21 April, the Erlangen AI Hub hosted an Industry Collaboration Day at the Department of Computer Science, University of Oxford. The event brought together academics from across the Hub network alongside leading industry partners, creating a valuable space for discussion, knowledge exchange and future collaboration.

The day opened with a welcome from Jeff Giansiracusa, Professor of Mathematics at Durham University. We were joined by an outstanding group of industry speakers, including Dr Carl Hunter (Durham Institute of Research, Development and Invention), Andreas Haggman (Ofcom), Danica Greetham (Capgemini Engineering), Francis Bursa (Oxford Nanopore Technologies) and Marco Albanese (Oxford Drug Design).

Academic perspectives were provided by Tom Coates, Professor of Mathematics at Imperial College London, and Pete Grindrod, Professor of Mathematics, University of Oxford.

The morning sessions highlighted the breadth of challenges and opportunities at the intersection of AI and industry. Topics ranged from online safety and the societal risks of AI, to the importance of sovereign AI capabilities in the UK and the role of collaboration between government, science and industry. Speakers also explored how AI is being applied to analyse complex data, identify patterns and accelerate progress in science and engineering.

Discussions continued over lunch, with participants exchanging ideas on future collaborations and exploring how partnerships between academia and industry can drive innovation and real-world impact.

In the afternoon, attendees worked in groups to develop ideas inspired by the morning sessions. These discussions generated a number of thought-provoking themes, including:

  • The evolving relationship between AI and philosophy, and whether the field is returning to its conceptual roots
  • Challenges in modelling complex, noisy and temporal data, and improving interpretability
  • The economics of benchmarking AI models and the risks of overfitting to established benchmarks
  • The role of domain expertise in mitigating risks for less-informed users of AI systems
  • Advances in machine learning for recognising complex patterns and improving sequencing accuracy

The day concluded with a panel discussion featuring Marika Taylor (University of Southampton), Ran Levi (University of Aberdeen) and Yue Ren (Durham University), who reflected on the future of AI and industry. The panel explored emerging challenges, key research questions, and how collaboration can deepen understanding of both mathematics and AI, while shaping their applications in industry.

The event received excellent feedback from participants. As Danica Greetham (Capgemini Engineering) noted:

“What stood out was the quality of the discussion afterwards—sharp questions and open exchanges with academics keen to dive quickly into the essence of problems. It was great to hear from other industrial partners about the challenges they’re tackling. A recurring theme: observational data doesn’t lie—but it rarely speaks plainly. Interpretation is where the real work happens.”

We look forward to our next major event where we can continue the conversations, Mathematical Foundations of AI: The Erlangen Hub Conference 2026, taking place from 1–3 September 2026 at the Mathematical Institute, University of Oxford. Early bird tickets are now available.

Meet the team Q&A: Marika Taylor

erlangenaihub on 27 March, 2026

In this Erlangen Hub Q&A we spoke to Marika Taylor, Co-Investigator and Theme C Deputy Lead. Marika is a Professor of Mathematics, Physics and AI at the University of Southampton. She trained in theoretical physics under Stephen Hawking, and is currently interested in geometric ML for fundamental physics applications and physics-inspired methods for ML. Marika was a Turing Institute Fellow and recipient of the “Dutch ERC” Vidi. She has a long track record with start-ups, including in encryption and fintech.  

Can you share a bit about your background and your current research focus?

My main research background is in mathematical and theoretical physics – particularly string theory, quantum theory and gravity. In parallel with this work in fundamental science, I have always been involved in mathematical modeling for real world problems, particularly finance, and have used neural nets for many years in that context. In recent years I’ve seen a convergence between my fundamental science research and my applied work: concepts from my areas of physics are being used within AI, while AI is increasingly being applied within fundamental physics too. A nice example would be graph neural networks in non-Euclidean geometry. Non-Euclidean geometry underpins our understanding of Einstein’s theory of general relativity (gravity). Many of the physical insights obtained from studying particularly geometries for gravity lead to insights into GNNs embedded into such geometries. Another example would be around symmetries. Physicists always build in their understanding of the underlying symmetries (exact or approximate) into their modelling of a system. One can similarly build symmetry equivariance into neural networks – for example, if you are classifying images of 3d objects and are agnostic about the orientation of the objects, then a network with rotational equivariance built into it will be more efficient in classification. My group is currently exploring more general symmetry equivariant networks, drawing from physics insights; this enables us to reduce substantially the number of parameters that need to be learned, and also to understand conceptually patterns found in previous algorithms. We are also interested in using physics understanding of time dependent systems to develop spiking neural networks; the latter are nature inspired, in that neurons only fire when a threshold is met, making them much more energy efficient.

What inspired you to pursue this area?

Throughout my career I have always worked on the frontiers of fundamental science. String theory is a “theory of everything”. It uses concepts from right across mathematics and also leads to new insights and ideas in mathematics – topological quantum field theory, for which Ed Witten won the Fields Medal, is a notable example. In parallel I’ve always enjoyed using the breadth of my knowledge in mathematical sciences for real world applications and I’ve often found that I get new insights into fundamental science from the applied work I’ve done. Over the last few years I’ve gradually moved more and more into AI, for both fundamental science and applied work, because there are so many exciting developments.

Which themes are you connected to within the Erlangen AI Hub and how does your work within the hub intersect with your research background?

The main theme that I am connected with is “Understanding Learning”, but I link with all the themes. Much of what I do relates to understanding conceptually hidden structures in data, and how geometry and topology can be used to characterize these. My physics insights into geometry also facilitate relating geometric and topological insights to real world phenomena.

What attracted you to the Erlangen AI Hub and what do you hope to see it achieve?

The hub is exploring the mathematical foundations of intelligence – this is essential to develop better, more efficient and safer models, which in turn will allow us to use AI in more contexts.

What’s been the most surprising or exciting finding in your work so far?

I don’t think that I would have predicted ten years ago that my two parallel streams of research would become so closely connected, with physics giving insights into developing AI and AI started to be used more in physics. (For AI to really be adopted more widely in physics, we will need robustness and accuracy.)

What challenges have you faced in your research, and how did you overcome them?

I like to take on research problems that are quite open ended and conceptually challenging. Inevitably that means that at times I get stuck or can’t quite see where to go next! Then I take a break, think about something else, and also talk to others, to get new ideas on where to go next.

What advice would you give to someone just starting out in your field?

I would advise somebody to follow their interests, and see where these take them!

Meet the team Q&A: Yue Ren

Kevin Childs on 16 February, 2026

In this Erlangen Hub Q&A we spoke to Yue Ren, Co-Investigator and Theme B lead at Durham University. Yue is a UKRI Future Leaders Fellow and leading expert in tropical geometry, mathematical software, and the application of both to neural networks and problems in industry and sciences. He is a core developer of the computer algebra systems Polymake, Singular, and OSCAR. 

What is your name?

Yue Ren

Can you share a bit about your background and your current research focus?

My background is in algebraic and tropical geometry.  I did my PhD in Germany, and spent some time in the US, South Africa, Israel, and Sweden before moving to the UK. My current focus is on applications of the latter to polynomial system solving and machine learning.

What inspired you to pursue this area?

Mathematically, I’ve always been fascinated by the concrete interplay between algebra, geometry, and combinatorics in tropical geometry.  However, I was always prone to making mistakes in hand calculations, so I decided to specialize in teaching a computer to do them for me instead.  Professionally, I wanted a path that combined my mathematical interests with practical skills like software development.

Which themes are you connected to within the Erlangen AI Hub and how does your work within the hub intersect with your research background?

I am mainly connected to Theme B, though my research touches upon other themes as well.  My work within the hub revolves around taking theoretical techniques from pure mathematics and turning them into practical algorithms. It’s a way to expand the machine learning toolbox with some interesting new tools.

What attracted you to the Erlangen AI Hub and what do you hope to see it achieve?

The Erlangen AI Hub brings together researchers from a wide range of backgrounds who are all pursuing a common goal. I’m really looking forward to the mathematical theories and practical tools that will come out of this unique mix of expertise.

What’s been the most surprising or exciting finding in your work so far?

I’ve found it really surprising that p-adic numbers, an abstract number system developed by pure mathematicians for number theory, can be so useful for data analysis. Their distance prioritizes structural relationships over physical proximity, which is perfect for hierarchical data.

What challenges have you faced in your research, and how did you overcome them?

Most researchers face the same problems: getting stuck on a proof, getting unstuck only to realize you’ve built a suspiciously complicated proof for a simple statement, and Reviewer 2.  Research is an endless chain of challenges, and the best strategy for overcoming them is to ask for advice, ask for feedback, and act on it.  Not only are advice and feedback valuable, but asking for and acting on them is also a valuable skill that needs to be trained.

What advice would you give to someone just starting out in your field?

Don’t just focus on doing things, reflect on how you do them. Finding better work habits will help you spend more time on the things you enjoy and less time on the things you don’t.

What’s something people might be surprised to learn about you outside of research?

I’ve participated in the Cape Argus Cycle Tour, a 110 km race around the Cape of Good Hope with 35k entrants. I finished in the middle of my age group while taking 300 pictures along the way. I was beaten by a group dressed up as the Power Rangers under the ruthless South African sun, but at least I managed to beat that one bloke who rode a unicycle.

Mathematics and the Future of AI

Kevin Childs on 12 February, 2026

Intellectual leadership through deep foundations

In a new University of Oxford Expert Comment article, Erlangen AI Hub Co-Investigator Professor Peter Grindrod CBE, argues that mathematics is not peripheral to artificial intelligence, but central to solving its core challenges.

As AI systems increase in scale and complexity, concerns around reliability, bias, interpretability, and formal guarantees cannot be addressed by engineering alone. Mathematics provides the structure to reason rigorously about uncertainty, optimisation, stability, and limits. Through probability, geometry, topology, dynamical systems, and information theory, maths enables AI systems that are interpretable by design and grounded in provable principles.

At the Erlangen AI Hub, Professor Grindrod and colleagues are working precisely in this space: bringing deep mathematical ideas into direct engagement with real-world AI challenges. Maths provides the foundation to build systems that are more robust, transparent, and intellectually grounded, helping position the UK as a leader through intellectual depth rather than scale. Read the full article below.

Expert Comment: How and why mathematics will both underpin and lead the next generation of AI | University of Oxford

Erlangen Hub Co-Investigators elected inaugural Fellows of the Academy for the Mathematical Sciences

Kevin Childs on 29 January, 2026

Erlangen Hub Co-Investigators Rama Cont and Christoph Reisinger have been elected to the inaugural cohort of Fellows of the newly founded Academy for the Mathematical Sciences. Their election recognises their leadership and contributions to the mathematical sciences and marks a significant milestone for both individuals and the Hub.

The Academy for the Mathematical Sciences brings mathematics to the centre of UK research, policy, and public life, advancing the discipline across multiple domains, including policy, education, research, and innovation. Sitting alongside other national academies, including the British Academy and the Academy of Medical Sciences, it will use its convening power to bring together experts to collaborate on major global challenges. These include climate change, national security, financial systems, and artificial intelligence.

The Fellowship comprises leading mathematicians from across academia, education, industry, business, and government, and includes Fields Medallists, senior figures in national security, and pioneers in computing and AI. The election of Rama and Christoph recognises their achievements and expertise within this distinguished community.

Rama Cont is Professor of Mathematics at the University of Oxford’s Mathematical Institute, Head of the Mathematical and Computational Finance Group, and a Fellow of St Hugh’s College. He also directs the Centre for Doctoral Training in Mathematics of Random Systems. His research spans stochastic computational methods, the mathematical foundations of AI, generative models, and data-driven modelling in finance. Alongside his academic work, Rama advises several AI-focused start-ups, including InstaDeep, 73Strings, and Synthera.AI. Through the Erlangen Hub, he contributes to strengthening the mathematical foundations that underpin modern AI systems and their applications. On knowledge of the election Rama said:

The Academy for the Mathematical Sciences’ ambitions are to represent and promote the full spectrum of mathematical sciences and their applications. As a mathematician with research activities spanning theory and applications, I am delighted to join the Academy as a Fellow.’

Christoph Reisinger is Professor of Applied Mathematics at the University of Oxford and specialises in stochastic simulation and control, mean-field models, and the mathematical foundations of deep learning. He collaborates closely with industry and government partners on challenges in AI security, air traffic control, and financial market microstructure. Within the Erlangen Hub, Christoph advances fundamental research at the interface of control theory and reinforcement learning, supporting the development of robust and reliable AI decision-making.

Hub PDRA Thom Badings receives AAAI doctoral award honourable mention

Kevin Childs on 27 January, 2026

Erlangen Hub researcher Thom Badings has received an honourable mention in the AAAI and ACM SIGAI Doctoral Dissertation Award; a prestigious international award recognising outstanding PhD research in artificial intelligence. As part of this recognition, Thom was invited to attend AAAI 2026 in Singapore, where he received the award and delivered an award talk on his doctoral research.

The AAAI and ACM SIGAI Doctoral Dissertation Award is jointly presented by the Association for the Advancement of Artificial Intelligence, and is regarded as one of the most significant distinctions for early-career researchers in the field. Honourable mentions are awarded to dissertations that demonstrate exceptional originality, technical depth, and potential impact.

In addition to the award presentation, Thom and Hub PDRA Francesco Fabiano also presented their joint research paper on robust decision-making, developed in collaboration with Co-investigators Alessandro Abate and Giuseppe De Giacomo.

Thom will be leaving the Erlangen AI Hub in March. His recognition at AAAI 2026 reflects both the strength of his individual research contributions and the broader impact of the Erlangen Hub’s work in artificial intelligence.