Find Academic Supervisors

Oscar Randal-Williams is the Sadleirian Professor of Pure Mathematics at the University of Cambridge, where he is affiliated with the Faculty of Mathematics and the Department of Pure Mathematics and Mathematical Statistics (DPMMS). His work is centered in the Differential Geometry & Topology research group, where he contributes to advancing knowledge in geometric and algebraic topology. Professor Randal-Williams specializes in Algebraic and Geometric Topology, with particular expertise in mapping class groups, moduli spaces, cobordism categories, spaces of manifolds, surgery theory, configuration spaces, characteristic classes, and K-theory. His research explores the deep connections between homotopy theory and geometric structures, with applications across various mathematical domains. His work often bridges abstract algebraic structures with concrete geometric problems, creating new frameworks for understanding topological phenomena. An analysis of Professor Randal-Williams' recent publications reveals a strong focus on homological stability phenomena, mapping class groups of high-dimensional manifolds, and the interplay between algebraic structures and geometric topology. His work frequently involves E ∞ -algebras, general linear groups, and the topology of diffeomorphism groups. A significant portion of his research investigates the structure of moduli spaces of manifolds and their connections to algebraic K-theory, with recent work extending to applications in mathematical physics through studies of symmetries in quantum field theories. Professor Randal-Williams maintains active collaborations with leading mathematicians worldwide, including Søren Galatius, Alexander Kupers, and Jeremy Miller, among others. His research has been published in top-tier mathematical journals including the Annals of Mathematics, Inventiones Mathematicae, and the Journal of the American Mathematical Society.

• Algebraic Topology
• Geometric Topology
• Mapping Class Groups
• +8 more

Jack Thorne is a Professor of Number Theory in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the University of Cambridge, within the Faculty of Mathematics. His office is located in room E1.18 at the department, and he can be contacted at thorne@dpmms.cam.ac.uk or by telephone at 01223 764283. Professor Thorne's primary research interests lie in Number Theory and Arithmetic Geometry , with significant contributions to the understanding of automorphic forms, Galois representations, and the Langlands program. His work spans theoretical developments in modularity, symmetric power functoriality, and the study of Selmer groups, demonstrating deep connections between algebraic geometry and number-theoretic phenomena. Analysis of Professor Thorne's recent publications reveals a consistent focus on advanced topics in modern number theory. His research demonstrates particular expertise in automorphy lifting theorems, potential automorphy over various fields, and the intricate relationships between Galois representations and automorphic forms. The publications show a progression toward increasingly sophisticated applications of the Langlands program to concrete arithmetic problems, with notable work on symmetric powers, level-raising phenomena, and the arithmetic of elliptic curves. Professor Thorne maintains an active research profile with numerous high-impact publications in leading mathematical journals including Annals of Mathematics, Publications mathématiques de l'IHÉS, and Journal of the American Mathematical Society. His collaborative work with prominent mathematicians such as Patrick Allen, Chandrashekhar Khare, and James Newton highlights his position within the international number theory community.

• Number Theory
• Arithmetic Geometry
• Automorphic Forms
• +3 more

Michael A Osborne is Professor of Machine Learning at the University of Oxford and leads the Bayesian Exploration Lab . He serves as Director of the EPSRC Centre for Doctoral Training in Autonomous Intelligent Machines and Systems and co-directs the Oxford Martin AI Governance Initiative. His research focuses on Bayesian optimization, Gaussian processes, and probabilistic numerics with applications in quantum devices, battery modeling, and AI governance. Key Positions: Professor of Machine Learning, University of Oxford Official Fellow, Exeter College Co-founder of Mind Foundry Lead Researcher, Oxford Martin Programme on Technology and Employment Research Themes: Probabilistic modeling for quantum systems Uncertainty quantification in energy storage AI safety and societal impact analysis Automated experimental design Quantum device calibration Probabilistic numerical methods Technical Contributions: Bridging reality gap in quantum devices Efficient Bayesian quadrature techniques Personalized neurostimulation algorithms Automated measurement protocols Quantum-classical hybrid ML

• Machine Learning
• Bayesian Optimization
• Gaussian Processes
• +3 more

Harvey Reall is a Professor of Theoretical Physics at the University of Cambridge , affiliated with the Department of Applied Mathematics and Theoretical Physics (DAMTP) and a Fellow of Trinity College . His research focuses on General Relativity and Effective Field Theory , particularly in the context of black hole mechanics , higher-dimensional gravity , and cosmic censorship . He has held prestigious positions including a Royal Society University Research Fellowship from 2005 to 2013. Education: PhD from DAMTP, University of Cambridge. Previous Appointments: Lecturer at the University of Nottingham (2005-2007); Postdoctoral positions at the Kavli Institute (2003-2005), Queen Mary University of London (2000-2003), and University of California, Santa Barbara (2003-2005). Reall's work explores the uniqueness and stability of black holes , causality in gravitational theories , and effective field theory approaches to gravity . His recent publications address nonperturbative second law formulations , event horizon dynamics , and axisymmetry theorems in extended theories of gravity. He has supervised numerous researchers including Aidan McSharry (2025-) , Maxime Gadioux (2022-) , and Iain Davies (2020-24) , contributing to the training of the next generation of physicists. Scientific Awards: Royal Society University Research Fellow (2005-2013)

• General Relativity
• Theoretical Physics
• Black Hole Mechanics
• +6 more

Professor Anders C. Hansen is a mathematician at the University of Cambridge and University of Oslo, leading the Applied Functional and Harmonic Analysis group. His work bridges functional analysis, artificial intelligence, and computational mathematics, focusing on the Solvability Complexity Index (SCI) hierarchy and stability issues in deep learning. He has held prestigious fellowships, including a Royal Society University Research Fellowship and Peterhouse Bye-Fellowship. Educated at the University of Cambridge, UC Berkeley, and the Norwegian University of Science and Technology Developed groundbreaking theories in compressed sensing and deep learning, revealing algorithmic instability paradoxes Organized workshops on computational mathematics and AI interpretability His research explores the SCI hierarchy , exposing computational barriers in AI, quantum mechanics, and inverse problems. Key projects include Smale’s 18th problem and analyzing neural network stability. His work has transformed understanding of compressed sensing, particularly in medical imaging. Recent scientific awards include the Whitehead Prize (2019), IMA Prize (2018), and Leverhulme Prize (2017). Collaborations span institutions like Caltech, MIT, and the University of Vienna. As an educator, he teaches NST Part IA Mathematical Methods , Part II Numerical Analysis , and a Part III course on Compressed Sensing . His group has mentored 17 PhD and postdoctoral researchers since 2012.

• Functional Analysis
• Artificial Intelligence
• Foundations of Computational Mathematics
• +15 more

Lukas Brantner is a Royal Society University Research Fellow at the Mathematical Institute of the University of Oxford. His research focuses on geometry, topology, and derived algebraic structures, with a particular emphasis on partition Lie algebras, deformation theory, and higher algebraic frameworks. His recent work spans topics such as derived foliations, Poincaré-Birkhoff-Witt theorems, and the complexity of geometric objects like Calabi-Yau varieties in characteristic p. This reflects a deep interplay between algebraic topology, homotopy theory, and modern algebraic geometry. Major Themes: Derived Algebraic Geometry, Homotopy Theory, Deformation Theory, Galois Theory Collaborators: Magidson, Nuiten, Antolín-Camarena, Heuts, Taelman, Campos, Waldron, Hahn, Knudsen, Mathew, Arone, Manners Scientific Awards & Honors: Royal Society University Research Fellow Brantner actively contributes to foundational research in algebraic topology and derived structures, often bridging pure algebra with topological phenomena. His publications highlight the evolution of partition Lie algebras, configuration spaces, and Goodwillie calculus in modern mathematics.

• Geometry
• Topology
• Algebraic Topology
• +4 more

Michael O'Boyle is a Professor at the University of Edinburgh's School of Informatics, where he serves as Director of the ARM Research Centre of Excellence and the EPSRC Centre for Doctoral Training in Pervasive Parallelism. Holding an EPSRC Established Career Research Fellowship, he leads pioneering work in compiler technology for heterogeneous architectures, bridging theoretical advances with practical high-performance computing applications. Professor O'Boyle's research spans multiple cutting-edge areas including heterogeneous code discovery and optimization, neural machine translation for program synthesis, deep neural network system stack optimization, software-defined hardware, and compiler/architecture co-design. His approach integrates constraint analysis, program synthesis, and machine learning to address complex challenges in high-performance computing across diverse hardware platforms. His recent publications reveal a strong trend toward integrating machine learning with traditional compiler techniques, particularly in neural program synthesis, tensor optimization, and architecture-aware compilation. This work represents a paradigm shift in compiler design, moving from rule-based systems to learning-based approaches that can automatically adapt to diverse hardware targets. IEEE/ACM CGO 2025 Distinguished Paper Award for 'Tensorize: Fast Synthesis of Tensor Programs from Legacy Code' IEEE/ACM CGO 2024 Test of Time Award ACM GPCE 2023 Best Paper Award for 'C2TACO: Lifting Tensor Code to TACOM' ACM ASPLOS 2021 Distinguished Paper Award IEEE HPCA 2021 Best Paper Award for 'Prodigy: Improving the Memory Latency of Data-Indirect Irregular Workloads' Professor O'Boyle has successfully mentored numerous PhD students who have secured prominent positions in academia (including at Cambridge, Edinburgh, Leeds, and McGill) and industry (including Meta, NVIDIA, Qualcomm, Huawei, and Microsoft). His research is supported by significant funding from EPSRC, ARM, and European projects including Bonseyes and Transmuter, demonstrating strong international recognition and industry impact. He leads the influential Compiler and Architecture Design (CArD) Group at the University of Edinburgh and is a founder of the HiPEAC Network of Excellence, which has grown into a major European initiative connecting researchers and practitioners in high-performance and embedded computing.

• Heterogeneous Code discovery and Optimisation
• Neural Machine Translation and Neural Synthesis
• Deep Neural Network system stack
• +7 more

Sam Staton is a Professor of Computer Science at the University of Oxford and Senior Research Fellow at Jesus College. He holds a Royal Society University Research Fellowship and leads the ERC-funded BLaSt project on probabilistic programming. His research focuses on programming language theory, particularly probabilistic and quantum programming, and category theory. Staton earned his PhD from the University of Cambridge in 2007, with prior roles as a lecturer and researcher at Cambridge, Paris, and Nijmegen. Research Interests: His work explores foundational aspects of programming languages, including semantics, algebraic effects, and applications to quantum computing and statistical modeling. Recent grants include the ARIA Safeguarded AI initiative and an AFOSR award. Education: PhD in Computer Science (2007), BA from Cambridge (2002). Students & Collaborators: Supervises multiple PhD students and postdocs, including those funded through his grants. Notable advisees include Swaraj Dash (now at Heriot-Watt) and Mathieu Huot (postdoc at MIT). Awards & Grants: Royal Society Fellowship, ERC Consolidator Grant (BLaSt), EATCS Best Paper Award, and Facebook Research Award. Labs & Teams: Leads the BLaSt project and collaborates on quantum programming via algebraic effects. Engaged in editorial roles for ACM Transactions on Quantum Computing and program committees for major conferences like POPL and LICS.

• Programming Language Theory
• Probabilistic Programming
• Quantum Computing
• +3 more

Hrvoje Jasak is a Professor of Continuum Physics at the Department of Physics (Cavendish Laboratory), University of Cambridge. He holds a fellowship at Christ’s College. His academic journey includes a BSc in Mechanical Engineering from the University of Zagreb (1992) and a PhD in CFD from Imperial College London (1996). Prior to academia, he held engineering roles at CD-adapco (now Siemens PLM), Nabla Ltd, and Ansys-Fluent Inc., contributing to CFD software development. His research focuses on numerical simulation methods, continuum physics, multiphase flows, naval hydrodynamics, and software development. He co-created OpenFOAM, chairs its Numerics Technical Committee, and leads the Computational Continuum Mechanics (CCM) research group within the Laboratory for Scientific Computing. His work integrates advanced numerical techniques like the partially rotating grid method, finite volume algorithms, and multiphysics coupling frameworks. Jasak is a seasoned developer with 25+ years of C++ expertise, having authored ~1 million lines of code. His group’s projects include the Naval Hydro Pack , fluid-structure interaction solvers, and the Eulerian multi-fluid model for dense sprays. He actively collaborates on international initiatives like the NUMAP-FOAM Summer School and the OpenFOAM community. His teaching spans MPhil programs, PhD supervision, and specialized CFD courses. Current research explores wave-ice interaction, lubricated contact modeling, and open-source software innovation. The CCM group’s work bridges academia and industry, addressing challenges in marine engineering, energy systems, and computational mechanics.

• Computational Fluid Dynamics (CFD)
• Continuum Mechanics
• Numerical Simulation Methods
• +5 more

Professor Jelena Grbic is a distinguished mathematician serving as Professor of Mathematics within the School of Mathematical Sciences at the University of Southampton since 2012. Her academic journey began with a B.Sc. in Mathematics from the University of Belgrade, Serbia in 1997, followed by a Ph.D. in Algebraic Topology from the University of Aberdeen in 2004. Prior to her current position, she held academic appointments at the University of Manchester (2007-2012) as Lecturer and Senior Lecturer, and at the University of Aberdeen (2004-2006) as Lecturer. Professor Grbic's research spans multiple interconnected domains of pure mathematics, with a primary focus on modern homotopy theory, particularly unstable homotopy theory, and its applications across topology, algebra, and geometry. Her work centers on decompositions and exponent problems in homotopy theory, homotopy aspects of Toric Topology, Hopf algebras, and geometric problems related to cobordisms and string topology. This research bridges abstract mathematical theory with potential applications in data science and computational topology. Analysis of her recent publications (2020-2025) reveals a consistent research trajectory in algebraic topology with increasing interdisciplinary connections. Her work demonstrates sophisticated mathematical techniques applied to complex topological structures, particularly moment-angle complexes and polyhedral products. Notably, her 2022 paper 'Aspects of topological approaches for data science' indicates growing interest in applying topological methods to contemporary data analysis problems, suggesting an expanding research horizon beyond pure mathematics. Professor Grbic actively supervises PhD students, including current student Salvatore Elia in Mathematical Sciences, and teaches modules covering algebraic topology and homotopy theory. She serves as a reviewer for prestigious journals including Homology, Homotopy and Application (2019), Transactions of the London Mathematical Society (2021), and The LMS Newsletter (2017), contributing to the scholarly community through peer review and academic service.

• Topology
• Algebra
• Combinatorics
• +6 more

Professor Imre Leader is a distinguished mathematician at the University of Cambridge, where he serves as Professor of Pure Mathematics in the Department of Pure Mathematics and Mathematical Statistics (DPMMS), which is part of the Faculty of Mathematics. His office is located in room C2.02 at the DPMMS building. Professor Leader's research primarily focuses on Extremal Combinatorics and Ramsey Theory , two fundamental areas of discrete mathematics. His work explores deep connections between combinatorial structures, set theory, and algebraic properties. He has made significant contributions to understanding partition regularity, monochromatic structures, extremal set theory, and combinatorial geometry. His research often bridges the gap between pure combinatorics and applications in computer science and theoretical mathematics. Over his prolific career, Professor Leader has published numerous influential papers in top mathematical journals, collaborating with leading mathematicians worldwide. His work spans various aspects of combinatorics including hypergraph theory, geometric combinatorics, additive number theory, and combinatorial game theory. He has been particularly active in advancing our understanding of Ramsey-type phenomena in infinite structures and developing new techniques in extremal combinatorics. Research Group: Combinatorics Email: I.Leader@dpmms.cam.ac.uk Telephone: 01223 765902 Personal homepage: https://www.dpmms.cam.ac.uk/~ibl10

• Extremal Combinatorics
• Ramsey Theory
• Combinatorial Number Theory
• +3 more

Brett Kolesnik is a Research Fellow in the Department of Statistics at the University of Warwick. His research focuses on probability theory, random structures, bootstrap percolation, and interactions with combinatorics. He has held postdoctoral fellowships at UC Berkeley, San Diego, and the University of Oxford, and was a Senior Demy at Magdalen College. His work includes organizing workshops on bootstrap percolation and collaborating with leading researchers in probability and combinatorics. Education: PhD in Mathematics from the University of British Columbia (advised by Omer Angel). Notable awards include the NSERC Postdoctoral Fellowship and the Florence Nightingale Bicentennial Fellowship in Statistics. Research interests span bootstrap percolation models, random graph dynamics, and stochastic processes. Recent work includes studies on Brownian map geometry, tournament score sequences, and Coxeter group structures. Selected articles explore topics such as critical beta-splitting processes, Catalan percolation, and random walks on algebraic structures. His publications appear in top journals like Electronic Journal of Probability and Annals of Applied Probability . Awards include the Florence Nightingale Fellowship and NSERC Postdoctoral Fellowship. Professional involvement includes organizing the 2024 BIRS workshop on Bootstrap Percolation and contributing to interdisciplinary collaborations in probability and combinatorics.

• Probability Theory
• Random Structures
• Bootstrap Percolation
• +4 more

Dr. Primoz Skraba is a Professor in Applied and Computational Topology at the School of Mathematical Sciences, Queen Mary University of London. As Deputy Head of the Centre for Probability, Statistics and Data Science, he bridges theoretical topology with practical applications in data analysis, machine learning, and optimization. Education : PhD in Electrical Engineering from Stanford University (2009) Prior Roles : Positions at INRIA, France; Jozef Stefan Institute, Slovenia; University of Primorska; University of Nova Gorica His research focuses on applying topological methods to analyze complex data. Key areas include: Stability of persistence diagrams for quantitative control in finite sampling Variants of persistence (zig-zag, robustness, multiparameter) Algorithmic Complexity in computational topology Stochastic Topology for random geometric models (Poisson, Boolean) Recent publications emphasize persistent homology in random geometric complexes, universality theorems, and integrating topological methods into machine learning. He received grants from the Leverhulme Trust, EPSRC, and Alan Turing Institute for projects on topological universality and AI foundations. His advisee Gabryel Mason-Williams explores wireless sensor network applications of homology.

• Applied Topology
• Geometry
• Algebra
• +5 more

Dr. Lucas Pahl is a Lecturer in Economics at the University of Sheffield, School of Economics since 2024. His research specializes in mathematical game theory, particularly in equilibrium refinements, fixed point theory, and real algebraic geometry. He holds a PhD in Economics from the University of Rochester, an MSc in Mathematics from IMPA (Brazil), and a BSc in Social Sciences from the University of São Paulo. Previous positions: Postdoctoral Scholar at Hausdorff Institute for Mathematics and Institute for Microeconomics, University of Bonn His research interests include advanced topics like fixed point theory applications in game theory, algebraic topology intersections with economic models, and equilibrium refinement methodologies. Recent work explores information spillover in zero-sum games and polytope-form game structures. Key publications focus on O’Neill’s theorem extensions, sustainable equilibria analysis, and finite characterizations of perfect equilibria. He serves as a reviewer for top journals including Econometrica and Games and Economic Behavior. No scientific awards explicitly mentioned. His advisory and grant activities remain unspecified in current records. Labs/teams: No lab affiliations explicitly stated in provided information.

• Mathematical Game Theory
• Fixed Point Theory
• Algebraic Topology
• +3 more

Gordon Plotkin is a Professor at the School of Informatics, University of Edinburgh, where he is affiliated with the Laboratory for Foundations of Computer Science (LFCS). His research lies at the intersection of theoretical computer science and programming language semantics, with a profound influence on the formal understanding of computation. His research interests include Programming Language Theory, Semantics of Programming Languages, Domain Theory, Operational Semantics, Lambda Calculus, Type Theory, Concurrency Theory, and Algebraic Effects. His seminal work on structural operational semantics and domain theory has laid the foundation for modern semantics of programming languages. His publications span over five decades, showing a sustained and evolving research trajectory from foundational work in lambda calculus and domain theory to recent contributions in algebraic effects, probabilistic computation, and biochemical systems modeling. The articles demonstrate a consistent focus on formal methods, mathematical rigor, and the algebraic structure of computational effects. He has collaborated with leading researchers including Martín Abadi, John Power, Glynn Winskel, and John Reynolds. His work continues to influence both theoretical and practical developments in programming languages and systems. Gordon Plotkin has made foundational contributions to computer science, particularly through his development of structural operational semantics and domain-theoretic models of computation. He has advised numerous researchers and supervised many influential PhD theses, though specific student names are not listed in the provided text. His work has been supported by long-standing affiliations with the Laboratory for Foundations of Computer Science and the University of Edinburgh, and he has contributed to major collaborative projects in programming language design and verification. He is associated with several research groups and labs, most notably the Laboratory for Foundations of Computer Science (LFCS), which serves as a hub for theoretical research in programming languages, semantics, and logic at the University of Edinburgh.

• Programming Language Theory
• Semantics of Programming Languages
• Domain Theory
• +7 more