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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

Manuel Del Pino is Professor at the University of Bath's Department of Mathematical Sciences and Royal Society Professor specializing in nonlinear partial differential equations. His research focuses on singularity formation, geometric evolution equations, and asymptotic analysis in fluid dynamics and mathematical physics. His investigations encompass blow-up phenomena in heat equations, vortex dynamics in Euler flows, and minimal surface theory. Current projects examine infinite-time singularity formation in parabolic equations and asymptotic properties of vortex configurations. Del Pino has received the Royal Society Professorship and leads multiple grants including 'Asymptotic patterns in nonlinear evolution problems' (EPSRC). He maintains collaborations with researchers globally through projects on singularity formation in PDEs.

• Nonlinear partial differential equations
• Singularity formation
• Mathematical analysis
• +2 more

Kenneth J. Falconer is the Regius Professor of Mathematics at the University of St Andrews, where he is a member of the School of Mathematics and Statistics and the Analysis Research Group. He has held prestigious positions at the University of Bristol and Corpus Christi College, Cambridge, and has been a visiting professor at institutions including Oregon State University and the Australian National University. Regius Professor of Mathematics, University of St Andrews (2017–present) Professor of Mathematics, University of St Andrews (1993–2017) Reader, University of Bristol Lecturer, University of Bristol Research Fellow, Corpus Christi College, Cambridge His research centers on fractal and multifractal geometry, geometric measure theory, and related fields. He has made seminal contributions to the understanding of fractal projections, dimensional analysis of self-affine sets, and fractal processes. His work includes the concept of the digital sundial and the introduction of the affinity dimension and Falconer’s distance problem. His research spans dimensional analysis, random fractals, PDEs on fractal domains, and combinatorial geometry. The most recent publications show a sustained focus on intermediate dimensions, projections of fractal sets and measures, and the dimensional properties of stochastic processes. His work frequently involves collaboration with leading mathematicians and appears in top journals such as Transactions of the American Mathematical Society , Ergodic Theory and Dynamical Systems , and Journal of Fractal Geometry . Fellow of the Royal Society of Edinburgh (1998) Shephard Prize, London Mathematical Society (2020) CBE, King’s New Year’s Honours (2024) Kenneth Falconer has supervised numerous students and collaborated with many researchers including Jonathan Fraser, Pertti Mattila, and Xiong Jin. He has served on editorial boards for Fractals , Journal of Fractal Geometry , and Mathematical Proceedings of the Cambridge Philosophical Society . He has been active in professional service, including as Chair of the British Mathematical Colloquium 2018 and Publications Secretary of the London Mathematical Society (2006–2009). He organized major programs at the Isaac Newton Institute and Mittag-Leffler Institute. He is also known for his involvement in the Long Distance Walkers Association, where he served as Chairman and Editor of Strider , and for his mathematical poetry featured in publications like the London Mathematical Society Newsletter .

• Fractal Geometry
• Geometric Measure Theory
• Multifractal Measures
• +6 more

Stephen Marshall is Professor of Urban Morphology and Urban Design at The Bartlett School of Planning, University College London. He also served as Visiting Professor at the Department of Architecture and Urban Studies, Politecnico di Milano, Italy from 2019 to 2021. With over twenty-five years of experience in the built environment fields, initially in consultancy and subsequently in academia, Professor Marshall has established himself as a leading expert in urban morphology and design. His educational background includes a Doctor of Philosophy from University College London (2001), a Postgraduate Diploma from Edinburgh College of Art (1995), a Master of Science from the University of Leeds (1989), and a Bachelor of Engineering from the University of Glasgow (1988). Professor Marshall's principal research focuses on urban morphology and street layout, examining their relationships with urban formative processes including urban design, coding and planning. His work bridges urban design theory with practical applications, exploring how cities evolve through complex interactions of physical form, social processes, and planning interventions. He has written or edited several influential books including 'Streets and Patterns' (2005), 'Cities, Design and Evolution' (2009), and 'Urban Coding and Planning' (2011). His recent publications reveal a growing interest in applying complexity science to urban morphology, with particular attention to biological analogies for understanding self-organizing cities. He has pioneered research on digital participation methods in urban planning, exploring how online platforms can enhance public engagement in urban space design. His work consistently bridges theoretical urban morphology with practical applications for contemporary urban challenges like pandemic adaptation and sustainable transport. Professor Marshall has served as Chair of the Editorial Board of Urban Design and Planning from its launch to 2012, and is now co-editor of Built Environment journal. His editorial work has significantly shaped scholarly discourse in urban planning and design. He leads several significant research initiatives including the Incubators of Public Spaces project, which explores digital platforms for co-creating urban spaces, and the Self-Organising Built Environment project, which investigates biological analogies in urbanism. These projects reflect his interdisciplinary approach to understanding and shaping urban environments, connecting with Sustainable Development Goal 11 (Sustainable Cities and Communities).

• Urban morphology
• Urban design
• Street layout and network structure
• +5 more

Prof Lars Olsen is a Professor in the School of Mathematics and Statistics at the University of St Andrews, based in the Mathematical Institute. His research focuses on fractal geometry, dynamical systems, and analysis, with particular emphasis on multifractal theory and metric number theory. He has supervised PhD student Luke Derry and has published extensively in peer-reviewed journals such as Monatshefte für Mathematik , Mathematische Zeitschrift , and Acta Mathematica Hungarica . His work explores intricate mathematical structures such as fractal dimensions, measure-theoretic properties of metric spaces, and applications to number theory. Recent studies include analyses of digit frequencies in infinite iterated function systems, exponential densities of integer subsets, and average distances in self-similar fractals. These contributions bridge pure mathematics with applications in understanding complex natural phenomena through geometric and analytic frameworks. Prof Olsen’s research portfolio demonstrates a strong focus on advanced mathematical analysis, with over 30 peer-reviewed publications since 2017 alone. His investigations into Hewitt-Stromberg measures and Gromov-Hausdorff-Prohoroff spaces exemplify his commitment to advancing foundational theories in fractal geometry and measure theory. Collaboration with international researchers has yielded multidisciplinary insights into topics like Lq-dimension analysis and topological dynamics of continuous functions.

• Fractal geometry
• Dynamical systems
• Analysis
• +3 more

Tom Leinster is a mathematician at the University of Edinburgh, specializing in category theory, metric geometry, and their applications to areas such as algebra, topology, and mathematical biology. His research focuses on the concept of magnitude, a measure for metric spaces and enriched categories, as well as entropy and diversity. He has authored influential books including *Basic Category Theory* and *Entropy and Diversity: The Axiomatic Approach*. Leinster's work bridges foundational mathematics with interdisciplinary applications, emphasizing the interplay between abstract structures and concrete problems. His research interests span category theory, metric geometry, algebraic topology, and mathematical biology. Key contributions include foundational work on magnitude and its connections to geometric measure theory, entropy characterization, and categorical frameworks for diversity measurement. Leinster also engages in mathematical education and ethics, advocating for responsible research practices. Notable publications include recent advancements in magnitude homology of Euclidean sets, extremal magnitude in metric spaces, and entropy modulo primes. His work often highlights interdisciplinary applications, such as biodiversity quantification and information-theoretic foundations.

• Category Theory
• Metric Geometry
• Algebra
• +3 more

Sergii Strelchuk is an Associate Professor of Computer Science at the University of Oxford, specializing in quantum computing and its applications. His research sits at the intersection of quantum information theory, computer science, and bioinformatics, with a focus on developing quantum algorithms for practical problems in genomics and beyond. Professor Strelchuk's primary research interests include quantum algorithms and their applications (particularly in bioinformatics), classical simulation methods for quantum computation, quantum complexity theory, and quantum learning theory. His work bridges theoretical quantum computing with practical applications, especially in the emerging field of quantum genomics and pangenomics, with significant implications for understanding human and pathogen genomes. His recent publications demonstrate a strong focus on applying quantum computing techniques to genomic data analysis, developing efficient fermion-qubit mappings for quantum simulation, and exploring fundamental aspects of quantum complexity theory. His research shows a clear trajectory toward making quantum computing practically applicable to biological data analysis and advancing our theoretical understanding of quantum computational models. Among his notable scientific achievements are: Royal Society University Research Fellow Leverhulme Early Career Fellow John and Delia Agar Research Fellow Professor Strelchuk leads several significant research projects including the Wellcome Leap "Human and Pathogen Quantum Pangenomics" project (2023-2026), which recently entered Phase 3 in April 2025, the EPSRC "Structure and symmetry in quantum verification" grant (2023-2025), and the "Quantum Algorithms for Quantum Field Theory" project (2022-2025). His research has attracted substantial funding for quantum computing applications in genomics. His work has received significant attention in both academic and popular science media, including coverage in Quanta Magazine and collaborations with institutions like the Sanger Institute to tackle complex genomic challenges using quantum computing approaches, with recent publicity about his leadership in the final phase of the Wellcome Leap-funded quantum pangenomics project.

• Quantum Algorithms
• Quantum Computing
• Bioinformatics
• +4 more

Prof. Andrea Mondino is a Professor at the University of Oxford 's Mathematical Institute , where he conducts research at the intersection of Analysis and Geometry with applications to Physics , Biology , and Economics . His work leverages techniques such as optimal transport , partial differential equations , and calculus of variations . His recent publications focus on synthetic Ricci curvature bounds , Lorentzian geometry , and RCD spaces , reflecting his expertise in geometric analysis and nonlinear PDEs . He has contributed to advancements in isoperimetric inequalities , Willmore surfaces , and metric measure spaces . Scientific Awards : Whitehead Prize 2020 ERC Starting Grant 2018 Bartolozzi Prize 2017 Huneke Fellow at MSRI-Berkeley 2016 Gioacchino Iapichino Prize 2014 ETH Fellow 2013-2015 Oberwolfach Leibniz Graduate Student 2012-2013 Benedetto Sciarra International Prize 2010 Marco Reni Prize 2009 Optime Prize 2007

• Analysis
• Geometry
• Optimal Transport
• +9 more

Cécile Mailler is a Reader in Probability at the University of Bath, where she is a member of the probability group Prob-L@B. She has held significant research positions including an EPSRC postdoctoral fellowship (2018-2021) titled "Random trees: analysis and applications" and previously worked as a postdoc at Prob-L@B (2013-2016) as part of Peter Mörters' EPSRC project "Emergence of Condensation in Stochastic Networks". She earned her PhD under the supervision of Brigitte Chauvin and Danièle Gardy at the Laboratoire de Mathématiques de Versailles. Her research focuses on probability theory with emphasis on branching processes, random trees, reinforcement mechanisms, Pólya urns, stochastic approximation, random networks, and statistical physics. She has made significant contributions to understanding preferential attachment models, zero-range processes, and random Boolean trees. Her work bridges theoretical probability with applications in statistical physics and combinatorics. Analysis of her recent publications shows a strong focus on random tree structures, branching processes, and reinforcement learning algorithms, with applications spanning from network theory to statistical mechanics. Her research demonstrates sophisticated mathematical techniques applied to complex stochastic systems, particularly those with reinforcement mechanisms and memory effects. Associate Editor of the Applied Probability Trust (since October 2020) Associate Editor of Stochastic Processes and Their Applications (since March 2022) Author of a general introduction to Pólya urns for the LMS Newsletter (November 2020) Co-organizer of the "Random Walks: Applications and Interactions" conference at CIRM (January 2026) She actively supervises PhD students working on topics including the multi-city ants process, Pólya urns with growing initial composition, large deviations for the Monkey walk, and competing growth processes. She has secured research funding through EPSRC fellowships and has been involved in multiple collaborative projects with prominent researchers in probability theory. Mailler regularly teaches mini-courses on advanced probability topics at international summer schools and workshops, demonstrating her commitment to knowledge dissemination in the field.

• Branching processes
• Random trees
• Reinforcement processes
• +9 more

Samuel Johnston is a Lecturer in Probability Theory at the Department of Mathematics, King's College London, affiliated with the Faculty of Natural, Mathematical & Engineering Sciences. He joined King's in 2022 after postdoctoral roles at the University of Bath, University of Graz, and University College Dublin. MMath, University of Oxford (2014) PhD in Probability, University of Bath (2017) Johnston's research spans probability theory, with a focus on stochastic processes involving branching, coalescence, and fragmentation. He actively explores free probability, random matrices, integrable combinatorics, and combinatorial approaches to the Jacobian conjecture. His work intersects with statistical physics and asymptotic geometric analysis. Recent publications highlight coalescent structures in heavy-tailed branching processes, integrable probability models, free probability via entropic transport, and convexity in high dimensions. Keywords include universality classes, Berry-Esseen bounds, and fragmentation-scaling limits. Samuel has not been mentioned to have received specific scientific awards or honors. He advises PhD students Rohan Shiatis (2023-) and Neil Mukerji (2024-). Collaborations span institutions in the UK, USA, Mexico, Austria, and Poland, with invited talks at global conferences including Xiangtan University, Imperial College London, and UCLA.

• Probability
• Stochastic Processes
• Free Probability
• +7 more

Dr. Mike Tehranchi is a faculty member at the University of Cambridge, affiliated with the Statistical Laboratory within the Department of Pure Mathematics and Mathematical Statistics (DPMMS) . His research focuses on mathematical finance, stochastic processes, and probability theory. He holds a Lecturer position and is actively involved in academic research, with notable contributions to financial models, term structure analysis, and stochastic calculus. His work bridges theoretical probability and applied finance, addressing topics such as interest rate modeling, implied volatility, and optimal investment strategies. Tehranchi’s research often intersects with optimization, statistical methods, and interdisciplinary applications in astrophysics and fluid dynamics. He maintains an active publication record and contributes to the academic community through his role in the Statistical Laboratory. Key research trends in his articles include the analysis of financial derivatives, stochastic processes in market dynamics, and the application of advanced mathematical techniques to real-world financial problems. His work emphasizes rigorous theoretical foundations while addressing practical challenges in quantitative finance. Dr. Tehranchi has no listed students or academic awards in the provided texts. He can be reached via email and is based in Room D1.04 at the Statistical Laboratory.

• Mathematical Finance
• Stochastic Analysis
• Probability Theory
• +3 more

Yang Li is a Royal Society University Research Fellow at the University of Cambridge, affiliated with the Department of Pure Mathematics and Mathematical Statistics within the Faculty of Mathematics. His research lies at the intersection of differential geometry, complex geometry, and mathematical physics, with a focus on foundational structures in string theory and mirror symmetry. Dr. Li's primary research interests center on Calabi-Yau metrics , special Lagrangian submanifolds , special holonomy , and gauge theory . His work explores the geometric behavior of Calabi-Yau manifolds under degeneration, addressing fundamental questions about metric collapse, diameter bounds, and the structure of singular limits. He has made significant contributions to the SYZ conjecture through constructions of explicit metrics and analysis of fibrations, while his gauge theory research examines singular connections and their topological implications. His publication record demonstrates a strong trajectory in geometric analysis, with recent work establishing uniform diameter bounds for collapsing Calabi-Yau metrics, developing non-Archimedean approaches to the SYZ conjecture, and proving uniqueness results for tangent cones of special Lagrangians. The research spans both theoretical developments in metric geometry and concrete constructions of geometric structures. Notable recognition includes the prestigious Royal Society University Research Fellowship , which supports his independent research program at Cambridge. Actively recruiting PhD students for October 2025 entry Research supported by Royal Society funding Dr. Li maintains an active research program within Cambridge's world-leading Department of Pure Mathematics and Mathematical Statistics, collaborating with leading geometers including Valentino Tosatti and Tristan Collins. His work bridges abstract geometric theory with applications to theoretical physics, particularly in understanding the geometric foundations of mirror symmetry.

• Calabi-Yau metrics
• Special Lagrangians
• Special holonomy
• +3 more

Professor Maciej Dunajski is a University Professor of Mathematical Physics at the Faculty of Mathematics, University of Cambridge, and a Senior Lecturer at Clare College Cambridge. His career spans institutions including Oxford and Cambridge, with roles ranging from Tutorial Fellow to Senior Research Associate. He holds a DPhil from the Mathematical Institute, Oxford, and was awarded the title of Professor by the President of Poland in 2011. University Professor of Mathematical Physics, Faculty of Mathematics, University of Cambridge (2021–present) University Reader in Mathematical Physics, University of Cambridge (2020–2021) Fellow at Clare College Cambridge (2003–present) Author of Solitons, Instantons & Twistors (Oxford University Press, 2009) His research focuses on Twistor Theory , Integrable Systems , and Differential Geometry , with significant contributions to self-dual gravity, Einstein-Weyl structures, and geometric solutions to nonlinear equations. His work bridges mathematics and theoretical physics, including applications to quantum gravity and black hole thermodynamics. Dunajski's recent publications highlight advancements in conformal geometry, null Kähler structures, and higher-dimensional relativity. His collaborations span researchers like K. P. Tod, R. Penrose, and L. Mason. He is based in Room B2.14 at DAMTP, Cambridge, and maintains an active research group in high-energy physics.

• Twistor Theory
• Integrable Systems
• Differential Geometry
• +3 more

Professor Tony Shardlow is affiliated with the Department of Mathematical Sciences at the University of Bath , UK. His research spans Stochastic Differential Equations , Bayesian Inverse Problems , Statistical Shape Modelling , and Numerical Analysis , with applications in data science, medical imaging, and computational physics. Labs/Teams : IMI (Institute for Mathematical Innovation), Prob-L@b (Probability Laboratory at Bath), SAMBa (EPSRC Centre for Doctoral Training in Statistical Applied Mathematics). Recent Research Trends : Focus on geometric shape analysis using flow fields, stochastic PDEs for particle dynamics, and Bayesian inference techniques in industrial and medical contexts. Collaborative work bridges computational mathematics with applications in hip dysplasia assessment and pesticide delivery systems. Advising : Supervised Fengpei Wang's PhD thesis on dimension reduction and Sinkhorn algorithms. Collaborates with researchers like N. D. F. Campbell and C. Poon. Teaching : Offers MA30170 - Numerical Solution of Elliptic PDEs.

• Stochastic Differential Equations
• Bayesian Inverse Problems
• Statistical Shape Modelling
• +3 more

Professor Igor Wigman is a Professor of Number Theory at King's College London, affiliated with the Department of Mathematics within the Faculty of Natural, Mathematical & Engineering Sciences. He completed his PhD in Number Theory at Tel-Aviv University under Zeev Rudnick, followed by postdoctoral roles at CRM Montreal and KTH Stockholm. He joined King's in 2012 as a Lecturer, becoming a Reader in 2014 and Professor in 2018. His research focuses on analytic number theory, probability, and mathematical physics, with emphasis on nodal lines, random fields, and quantum chaos. Notable contributions include studies on the Gauss circle problem, eigenvalue clusters, and nodal volume distributions of random functions. Wigman co-organized the 2016 'Random Waves in London' workshop and delivered an inaugural lecture in 2023 on the interplay of number theory, random functions, and music geometry. His work bridges pure mathematics with applications in spectral geometry and stochastic processes.

• Analytic Number Theory
• Probability and Stochastic Processes
• Mathematical Physics
• +4 more