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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

Dr. Paul Mitchener is a Lecturer at the University of Sheffield within the School of Mathematical and Physical Sciences . He serves as the MSc Mathematics Admissions Tutor and Course Director , contributing to both research and postgraduate education. His research lies at the intersection of Algebraic Topology and Functional Analysis , with a focus on non-commutative geometry, K-theory, index theory, and coarse geometry. He has explored applications of these areas to problems in operator algebras and topology, particularly through work on the Baum-Connes conjecture, Novikov conjecture for semigroups, and coarse homotopy groups. The 15 most recent publications highlight trends in his work: (1) Coarse Geometry (2020, 2001), (2) Novikov Conjecture (2018, 2011), (3) KK-Theory and C*-Categories (2002, 2007), (4) E-Theory (2020), and (5) Descent Techniques (2012, 2010). These works frequently involve analytical methods in topological problems.

• Algebraic Topology
• Functional Analysis
• Non-Commutative Geometry
• +7 more

Professor Zdzislaw Brzezniak is a Professor in the Department of Mathematics at the University of York, where he has been since 2005. He holds a PhD in PDEs from Jagellonian University, Krakow (1988). His research focuses on stochastic partial differential equations (SPDEs), turbulence, geometric analysis, and harmonic analysis, with notable contributions to Navier-Stokes and Euler equations. He has organized major international workshops, including events on stochastic PDEs at ICMS (Edinburgh) and the Isaac Newton Institute. Education: PhD in PDEs (Jagellonian University, 1988). Research Interests: SPDEs, stochastic geometric problems (e.g., Landau-Lifshitz equations), fluid dynamics, and applications in physics. His work bridges pure and applied mathematics, influencing theoretical frameworks in micromagnetism and quantum field theory. Key Awards: 2013 Best Paper Award, 1st Prize, Institute of Information Theory and Automation. Supervision: Advised over 10 PhD students, including Nimit Rana (2019) and Fabian Hornung (2018). Current students include Asma Alalyani and Hessa Alharbi. Active in mentoring across stochastic analysis and geometric PDEs. Labs/Groups: Member of Mathematical Finance and Stochastic Analysis Research Group, and Geometry and Analysis Research Group at the University of York.

• Stochastic Partial Differential Equations
• Turbulence
• Geometric Analysis
• +5 more

Mark Kambites is a Professor of Pure Mathematics at the University of Manchester , affiliated with the Department of Mathematics. His research focuses on semigroup theory, tropical algebra, geometric group theory, and formal languages. He holds roles including membership in the EPSRC Strategic Advisory Team (SAT) and editorial positions in journals like the International Journal of Algebra and Computation. Education: M.Math. Mathematics and Computer Science, University of York (2000) Ph.D. Pure Mathematics, University of York (2003) Research Interests: Kambites explores semigroup structures, tropical algebra's applications, and interactions between algebra and geometry. Key areas include matrix semigroups over tropical semifields, combinatorial group theory, and computational complexity. His work bridges pure mathematics and theoretical computer science. Grants and Collaborations: Leads the Centre for Digital Trust and Society (EPSRC-funded) and collaborates internationally. Serves as central organizer of the North British Semigroups and Applications Network (NBSAN). Affiliations: Active in the Algebra Group, Tropical Mathematics Group, and Data Science Institute at Manchester. Supervises PhD/MSc students in algebraic and computational mathematics.

• Semigroup Theory
• Tropical Algebra
• Geometric Group Theory
• +5 more

Dr Paul C. Bell is a Research Fellow in Computer Science currently affiliated with Liverpool John Moores University since 2017, maintaining a continuing Visiting Fellow position at Loughborough University where he previously served as a lecturer from 2011 to 2017. His academic foundation includes postdoctoral research at Turku University (Finland), Universite catholique de Louvain (Belgium), and Liverpool University following doctoral studies. His educational background comprises: BSc, University of Liverpool PhD, University of Liverpool Dr Bell specializes in Theoretical Computer Science and Formal Language Theory, investigating the boundaries of tractability and computability for reachability problems across mathematical models including matrix semigroups, hybrid systems, and probabilistic/quantum automata. His interdisciplinary work bridges Computer Science, Physics, and Mathematics through encodings of optimization problems for adiabatic quantum computers, alongside contributions to energy-efficient computing via speed-scaling algorithms for multi-processor systems. With over twenty publications in leading international venues, he actively serves as a reviewer and program committee member for conferences such as Reachability Problems 2017.

• Theoretical Computer Science
• Formal Language Theory
• Reachability Problems
• +8 more

Dr. Alexei Vernitski is a Senior Lecturer in the School of Mathematics, Statistics and Actuarial Science (SMSAS) at the University of Essex. His research focuses on applying artificial intelligence (including reinforcement learning and deep learning) to mathematical problems in knot theory, algebra (e.g., braid theory), and universal algebra. He also explores mathematics education, particularly enhancing student motivation. Previously, he worked in the financial sector as a programmer and as a computer science lecturer. His research interests span AI-driven knot theory, algebraic structures (semigroups, groups), and mathematics education. Notable areas include the application of neural networks to braid untangling, automated reasoning in knot diagrams, and cognitive studies on math anxiety using EEG. He has supervised PhD students in mathematics education, universal algebra, and computer science applications of mathematics. His recent work demonstrates trends in combining machine learning with topological and algebraic problems, emphasizing practical AI solutions for abstract mathematical challenges. His articles reflect interdisciplinary approaches, merging computer science techniques with pure mathematics. Dr. Vernitski has advised multiple PhD students, contributing to diverse fields from knot theory to educational technology. His work bridges theoretical mathematics with real-world applications, such as optimizing data transmission and enhancing learning systems through neuroadaptive methods.

• Artificial Intelligence
• Knot Theory
• Algebra
• +3 more

Joachim Zacharias is a Professor of Mathematics at the University of Glasgow, affiliated with the School of Mathematics and Statistics. His primary research focuses on operator algebras, C*-algebras, noncommutative geometry, and ergodic theory. He has held significant grants totaling £531,750 and contributed to numerous EU and non-EU research networks. Zacharias has organized major events such as the LMS Regional Meeting & Workshop on C*-Algebras and the CSTAR conference. He has supervised seven PhD students and co-authored over 25 publications. Education: No specific education details provided. Research Interests: C*-Algebras, Ergodic Theory, Operator Theory, Noncommutative Geometry, Approximation Properties of Algebras. Grants & Service: Extensive refereeing for journals, external examiner for multiple PhD programs, and grant holder for projects like EPSRC grants. Publications: Recent work includes studies on Cuntz semigroups, nuclear dimension, Rokhlin dimension, and spectral triples. His research spans operator algebras, noncommutative geometry, and functional analysis. Conferences: Organized workshops and seminars, including the North British Functional Analysis Seminar and the Fields Institute Workshop. Advising: Supervised students such as Andrew Hawkins (spectral triples) and Luke Hamblin (Rokhlin dimension).

• C*-Algebras
• Ergodic Theory
• Operator Theory
• +4 more

Dr Alexei Lisitsa is a Senior Lecturer at the University of Liverpool specializing in theoretical computer science and mathematical structures. His work bridges automated reasoning, machine learning, and topological mathematics with applications in cybersecurity and network analysis. Active since at least 2008, he maintains a robust research profile with recent publications through 2025. His research focuses on computationally intensive problems in algebraic topology and formal methods. Key contributions include developing machine learning techniques for braid invariants, automating group theory proofs, and creating knot diagram analysis frameworks. This work consistently integrates experimental mathematics with computational verification, demonstrating innovative cross-disciplinary approaches to complex topological challenges. Analysis of his 2023-2025 publications reveals accelerating integration of neural networks with symbolic reasoning systems. His team pioneers applications of deep learning to traditionally intractable problems in braid theory and group presentations, while maintaining strong foundations in formal verification methods for temporal logic systems. Dr Lisitsa actively secures competitive research funding: Flexible Querying of Encrypted Graph Databases (Innovate UK, 2020) KTP with ValueChain Enterprise Systems (Innovate UK & VALUECHAIN, 2018-2022) Future AI and Robotics for Hub Space (FAIR-SPACE) (EPSRC, 2017-2021) Machine Learning for recognising tangled 3D objects (Leverhulme Trust, 2020-2023) Engineering Autonomous Space Software (EPSRC, 2008-2012) Discrete analogues of dynamical systems (NATO, 2008-2010) He supervises postgraduate research in network security and movement pattern analysis, with thesis topics including temporal logic-based intrusion detection systems and large-scale network prediction methodologies.

• Automated Reasoning
• Machine Learning
• Knot Theory
• +3 more

Brent Everitt is a Professor in the Department of Mathematics at the University of York, where he has been since 1999. He holds a Readership position and has previously held roles such as Senior Lecturer. His academic journey includes undergraduate studies at the University of Auckland, followed by postgraduate degrees at the University of Toronto and the University of Auckland. Before joining York, he held positions at the Universities of Aberdeen, Warwick, and Durham. Everitt’s research focuses on algebra, topology, and combinatorics, with a particular emphasis on homological methods in algebra, partial symmetry through reflection monoids, representation theory of groups and monoids, and geometric manifolds. Collaborators include Paul Turner, John Fountain, and James East. His work on hyperplane arrangements, matroids, and Coxeter groups has led to significant contributions in algebraic topology and geometric group theory. He has supervised eight PhD students, including Majed Albaity and Jim Woodward. His research projects include exploring sheaf homology, minimal hyperbolic manifold volumes, and the interplay between combinatorial structures and algebraic frameworks. He has been involved in grants such as the Heilbronn small grant scheme on diagrammatic intuition and deep learning in mathematics. Everitt is actively engaged in academic outreach, delivering invited talks globally on topics like reflection monoids, Khovanov homology, and hyperbolic manifolds. His teaching contributions include courses on Galois theory and algebraic topology, reflecting his dedication to both research and education.

• Algebra
• Topology
• Combinatorics
• +3 more

Jim Renshaw is an Associate Professor in the Mathematics department at the University of Southampton, where he conducts research in algebraic semigroup theory with particular emphasis on actions of semigroups and monoids on sets and ordered structures. Renshaw's primary research interests include: Algebraic semigroup theory and its applications Actions of semigroups and monoids on sets and ordered structures Semigroup amalgams and homological classification theory of monoids Flat covers and pre-covers of monoid acts Structure and actions of E-dense and E-inversive semigroups Discrete log problem and its connections with semigroup theory His publication record shows a clear progression in his research focus, beginning with foundational work on semigroup amalgams and flat covers of monoid acts, then expanding to investigate inverse semigroup actions on graphs and trees, and most recently exploring connections between E-dense semigroups and the discrete log problem. His 2024 paper 'Semilattices of stratified extensions' represents the current direction of his research in ordered algebraic structures. Renshaw is actively involved in doctoral supervision, currently mentoring William Lee Warhurst who is pursuing an iPhD in Mathematical Sciences. He has indicated that he is accepting applications from prospective PhD students. His teaching interests are concentrated in algebra and number theory, contributing to the mathematics curriculum at the University of Southampton.

• Algebraic semigroup theory
• Actions of semigroups and monoids on sets
• Actions of semigroups and monoids on ordered structures
• +5 more

Dr James Cranch is a Teaching Fellow in the School of Mathematical and Physical Sciences at the University of Sheffield, holding critical roles as Chair of Schools Liaison, Disability Liaison Officer, Outreach Officer, and Tutor for Men Students. Based in G39c, Hicks Building, he actively contributes to academic administration and student support services. His research centers on homotopy theory and category theory, with significant interdisciplinary extensions into theoretical computer science. Key focus areas include concurrency theory, monoidal category applications, and homotopy type theory, demonstrating consistent exploration of algebraic structures in computational contexts since 2010. Recent publications (2020-2024) reveal a concentrated effort on convolution frameworks for concurrency, interacting monoidal systems in computing, and cohomological studies of partition algebras. These works, published in venues like Mathematical Structures in Computer Science, highlight his bridging of abstract mathematics with practical computing challenges through collaborations with Struth, Doherty, and others.

• Homotopy theory
• Category theory
• Theoretical Computer Science
• +3 more

Andre Henriques is a Professor at the Mathematical Institute of the University of Oxford, located in the Andrew Wiles Building of the Radcliffe Observatory Quarter. His research focuses on Conformal field theory, Algebraic topology, Operator algebras, and Representation theory. He is affiliated with the Functional Analysis and Topology research groups. Recent work includes publications on W*-categories, Segal-Neretin semigroups, and planar algebras. His research bridges advanced mathematical structures with applications in theoretical physics and quantum topology. Henriques maintains a professional website at andreghenriques.com and is registered with ORCID (ID: 0000-0002-7804-8421 ). His recent publications emphasize categorical frameworks, geometric group theory, and operator algebraic techniques, reflecting a deep engagement with foundational mathematical problems. No formal advising or grant details are highlighted in the provided text.

• Conformal field theory
• Algebraic topology
• Operator algebras
• +1 more

O. Deniz Akyildiz is an Assistant Professor in Statistics at the Department of Mathematics, Imperial College London. His research focuses on computational statistics, machine learning, and generative modelling, with applications to sampling, optimization, and inverse problems. He holds affiliations with the Artificial Intelligence Network and Mathematics research groups. Previously, he obtained degrees in Electronics and Communications Engineering from İTÜ, followed by a PhD in Signal Processing at Universidad Carlos III de Madrid. Before joining Imperial, he worked as a postdoctoral researcher at Warwick CS and The Alan Turing Institute. His research interests span diffusion-based parameter estimation, score-based generative models, Langevin dynamics for optimization, and adaptive importance samplers. Recent work includes contributions to latent diffusion models, Sinkhorn semigroups, and stochastic filtering techniques. Notable publications include works on statistical finite elements, interacting particle Langevin algorithms, and physics-informed deep generative models. His technical blog almost stochastic and GitHub repository provide further insights into his research.

• Computational Statistics
• Machine Learning
• Generative Modelling
• +7 more

Jacek Banasiak is a Visiting Professor in the Department of Mathematics and Statistics within the Faculty of Science at the University of Strathclyde, United Kingdom. He is actively engaged in research in mathematical analysis, particularly in the theory of semigroups and its applications to coagulation-fragmentation processes. His research focuses on coagulation and fragmentation dynamics , semigroup theory , and kinetic models , with applications in population dynamics and engineering mathematics. His work often involves rigorous analysis of integro-differential equations, unbounded operators, and long-term behavior of solutions. He frequently collaborates with Wilson Lamb and other mathematical analysts. The most recent publications demonstrate sustained contributions to the solvability, compactness, and asymptotic analysis of coagulation-fragmentation equations, particularly under power-law and strong fragmentation regimes. His work bridges pure and applied mathematics, contributing to both theoretical developments and modeling in physical and biological systems. The following scientific contributions have been recognized through peer-reviewed publications: Development of analytic fragmentation semigroups Existence and uniqueness results for equations with unbounded rates Study of asynchronous exponential growth in discrete and continuous models Analysis of mass loss in coagulation-fragmentation systems Banasiak has advised students and researchers in the field of mathematical modeling, though specific names are not listed in the source material. There is no mention of external grants or funding sources in the provided texts. He is associated with a research group focused on kinetic theory and evolution equations at Strathclyde.

• Mathematical Analysis
• Semigroup Theory
• Coagulation and Fragmentation Processes
• +5 more

Gemma Crowe is a Heilbronn Fellow in Pure Mathematics, focusing on advanced research in combinatorial and geometric group theory. Her work addresses decision problems, conjugacy growth, formal language theory, and semigroups. She actively contributes to the theoretical foundations of group theory and its intersections with topology and algebra. Her research interests revolve around the structural properties of groups, particularly dihedral Artin groups, automorphism groups of free groups, and conjugacy languages. These topics explore the interplay between algebraic structures and geometric/topological frameworks, with applications in understanding group dynamics and language formalisms. Recent work highlights include studies on conjugacy geodesics in Artin groups, twisted conjugacy in torus knot groups, and the topology of automorphism groups. These contributions advance the field's understanding of group behavior and its computational aspects.

• Combinatorial Group Theory
• Geometric Group Theory
• Decision Problems
• +3 more