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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

Bei Wang Phillips is an Associate Professor in the School of Computing and a faculty member at the Scientific Computing and Imaging (SCI) Institute at the University of Utah. She holds a Ph.D. in Computer Science from Duke University and an undergraduate degree from the University of Bridgeport. Her research focuses on Topological Data Analysis (TDA), data visualization, computational topology, and machine learning, with applications in scientific data exploration and analysis. She has received prestigious awards including the NSF CAREER Award (2022) and the PECASE Award (2025). Her work spans projects funded by NSF, NIH, and DOE, including multiparameter TDA and topology-aware data compression. She advises numerous students and collaborates on interdisciplinary initiatives in astrophysics, climate science, and AI fairness. Education: Ph.D. in Computer Science, Duke University (2010) B.S. in Computer Science and Mathematics, University of Bridgeport (2003) Research Interests: Topological techniques for large-scale data analysis Integration of topological, geometric, and machine learning methods Applications in visualization, bioinformatics, and network analysis Key Projects: NSF-funded TDA research (DMS-2301361, OAC-2313124) DOE project on topology-preserving data compression Collaborations with NASA, Argonne National Lab, and Carnegie Institution of Washington Awards: Presidential Early Career Award for Scientists and Engineers (2025) NSF CAREER Award (2022) DOE Early Career Research Program (2020) Advising and Grants: Mentored over 30 students and postdocs Recipient of multiple NSF and DOE grants totaling millions

• Topological Data Analysis
• Data Visualization
• Computational Topology
• +5 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

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

Dr. Konstantin (Kostia) M. Zuev serves as Teaching Professor in the Computing + Mathematical Sciences Department at California Institute of Technology , where he has made significant contributions to network science and computational statistics since 2016. His dual PhDs in Mathematics (Moscow State University, 2008) and Civil Engineering (HKUST, 2009) underpin his interdisciplinary research spanning differential geometry, stochastic simulation, and network dynamics. Education PhD in Mathematics, Lomonosov Moscow State University (2008) PhD in Civil Engineering, Hong Kong University of Science & Technology (2009) His research focuses on network science , particularly course-prerequisite networks and complex financial systems , with recent work extending to network navigability in cosmological models and rare event simulation. Over his career, he has developed innovative Bayesian inference methods and geometric preferential attachment theories while maintaining active collaborations across mathematics, physics, and biomedical domains. Recent publications highlight network analysis in education ( 2023 ), hyperbolic graph theory ( 2024 ), and pandemic-informed cancer mortality studies ( 2023 ). His 15 most recent articles demonstrate methodological innovations across disciplines including statistics, physics, finance, and cosmology. Scientific recognition includes Humboldt Research Fellowship (2021) Carver Mead Seed Fund Grant (2023) ASCIT Teaching Award (2018, 2023) Northrop Grumman Teaching Excellence Prize (2019) As Graduate Option Representative for Information and Data Sciences at Caltech and faculty advisor for multiple student organizations including the Caltech Karate Club and Caltech Chess Club , he actively bridges academic rigor with community engagement through outreach initiatives like the virtual math education channel and university math circles for K-12 students.

• Network Science
• Applied Probability
• Computational Statistics
• +4 more

David Perkinson is a Professor of Mathematics at Reed College, where he holds a position in the Department of Mathematics. His research focuses on combinatorics, algebraic geometry, and discrete mathematics, with a particular emphasis on sandpile models, graph theory, and matroid theory. He is the author of the textbook *Divisors and Sandpiles: An Introduction to Chip-Firing*, which explores the combinatorial theory of chip-firing on graphs. Perkinson has also developed software tools like the Sandpile Java App, which visualizes and analyzes the Abelian Sandpile Model. He organizes the Cascade Lectures in Combinatorics (CALICO), a series of conferences funded by the National Science Foundation, aimed at fostering collaboration among researchers in combinatorics. His work bridges discrete mathematics with algebraic geometry, emphasizing connections between graph theory and geometric structures. Perkinson teaches advanced courses in analysis and contributes to the academic community through his research on topics such as divisor theory on graphs, sandpile groups, and combinatorial game theory. His recent publications (2015–2024) address matroid theory, sandpile dynamics, and applications of algebraic methods to discrete systems.

• Combinatorics
• Graph Theory
• Algebraic Geometry
• +5 more

Prof. Dr. Ieke Moerdijk is a distinguished Professor of Mathematics at the Mathematical Institute of Utrecht University, part of the Faculty of Science. Previously, he held positions at Radboud University (2011–2016) and has been affiliated with institutions like the University of Chicago, Cambridge, and the University of Amsterdam, where he earned his PhD in Mathematics (1985, Cum Laude). His research focuses on algebraic and differential topology, homotopy theory, and applications of topological structures to mathematical logic. He is renowned for co-authoring influential books such as Sheaves in Geometry and Logic (with S. Mac Lane) and Introduction to Foliations and Lie Groupoids (with J. Mrcun). Moerdijk has received prestigious awards including the Spinoza Prize (2012) and the Descartes-Huygens Prize (2011), and is a member of the KNAW and Academia Europaea. His current research emphasizes the theory of dendroidal sets and homotopy operads. He has held visiting positions at institutions like Cambridge, McGill, and Sydney. His academic contributions span editorships, teaching, and supervising numerous students. Moerdijk’s work bridges foundational mathematics with advanced categorical and topological frameworks, influencing areas from algebraic geometry to logic. Education: Bachelor’s/Master’s in Mathematics, Philosophy, and Linguistics at University of Amsterdam PhD in Mathematics, University of Amsterdam (1985) Awards: Spinoza Prize (2012), Descartes-Huygens Prize (2011) Member of KNAW (2006), Academia Europaea (2014) Huygens Fellowship (1986), PIONIER Grant (1995) Research Interests: Algebraic topology, homotopy theory, operads, category theory, and mathematical logic. Moerdijk’s publications include foundational works on dendroidal sets and simplicial methods, with recent contributions addressing ∞-operads and univalent completion. His research often explores connections between algebraic structures and topological spaces, with applications to higher category theory.

• Algebraic Topology
• Differential Topology
• Mathematical Logic
• +3 more

Gil Kalai is a Professor of Mathematics at the Hebrew University of Jerusalem since 1992, where he holds the Henry and Manya Noskwith Chair. He also serves as an Adjunct Professor of Mathematics and Computer Science at Yale University since 2004 in a long-term part-time visiting position. His academic career includes visiting positions at prestigious institutions including MIT, Cornell, IAS Princeton, Berkeley, Bell-labs, IBM, and Microsoft. Professor Kalai's research spans multiple areas within mathematics and theoretical computer science. His work in combinatorics encompasses geometric, probabilistic, and topological approaches. He has made significant contributions to the study of convex sets and polytopes, linear programming, and theoretical computer science. His influential 1988 paper with Kahn and Linial on Boolean functions pioneered applications of Fourier analysis in theoretical computer science. Kalai's research has evolved to include the application of Fourier analysis to thresholds, influences, symmetries, noise, percolation, and social choice. He has developed theories in algebraic shifting and studied face-numbers and other combinatorial invariants of polytopes. His work on the diameter of polytopes and randomized simplex algorithms has been influential in optimization theory. In 1993, his collaboration with Kahn produced a groundbreaking counterexample to Borsuk's Conjecture in 1325 dimensions. Professor Kalai's publications reveal a consistent focus on the intersection of combinatorics, geometry, and theoretical computer science. His work shows a progression from foundational combinatorial geometry to increasingly sophisticated applications of harmonic analysis in discrete mathematics. The recurring themes across his 30+ year career include Boolean functions, polytope theory, and probabilistic methods in combinatorics, demonstrating remarkable coherence in his research trajectory. 2016 European congress of Mathematics, plenary speaker 2013 ERC advanced grant 2012 Rothschild Prize 1994 International Congress of Mathematicians invited section talk, Zurich 1994 Fulkerson Prize 1993 Erdos Prize 1992 Polya Prize Though specific details of his advising are not provided in the source material, Kalai has written over 70 scientific papers and maintains an active research blog entitled "Combinatorics and More." His 2013 ERC advanced grant indicates significant research funding for his work. His extensive collaborations with researchers across multiple institutions suggest a robust research program with numerous PhD students and postdoctoral researchers, though specific names are not mentioned in the provided texts. Professor Kalai maintains active research connections across multiple institutions including Hebrew University, Yale, and various research centers worldwide. His work bridges pure mathematics and theoretical computer science, creating a unique interdisciplinary research environment that influences both fields.

• Combinatorics
• Geometric Combinatorics
• Probabilistic Combinatorics
• +7 more

Aaron Smith is an Associate Professor in the Department of Mathematics and Statistics at the University of Ottawa, affiliated with the Faculty of Science. He holds a PhD from Stanford University. His research focuses on applied probability, computational statistics, Monte Carlo methods, and Markov chains, with an emphasis on advancing theoretical understanding and practical applications of these methodologies. Dr. Smith's work includes contributions to community detection algorithms, Markov chain mixing times, and synthetic health data generation. His recent publications explore topics such as nonstandard Dirichlet form representations, perturbation analysis of MCMC algorithms, and sparse Bayesian multidimensional scaling. He advises students in applied probability and has supervised postdoctoral researchers in related fields. His research interests span a wide range of topics, including stochastic processes, statistical inference, and algorithm design. He is particularly known for his analysis of convergence rates in Markov chains and the development of efficient sampling techniques for complex models. His interdisciplinary work bridges theoretical mathematics and practical computational challenges in data science and healthcare. Dr. Smith collaborates on projects involving synthetic data frameworks for privacy-preserving applications and has contributed to foundational work on mixing times and perturbation effects in stochastic systems.

• Applied Probability
• Computational Statistics
• Monte Carlo Methods
• +3 more

Julie Bergner is a Professor in the Department of Mathematics at the University of Virginia. She is currently on sabbatical during 2024-25 as a Visiting Fellow at Clare Hall, University of Cambridge. Her research focuses on Homotopy Theory, Algebraic Topology, Algebraic K-Theory, and Category Theory, with a particular emphasis on higher category theory and homotopical algebraic structures. University of Virginia (Professor, Department of Mathematics) University of Cambridge (Visiting Fellow at Clare Hall, 2024-25) Her work spans 2-Segal objects, model categories, Waldhausen constructions, and applications to topological field theories. She has received NSF CAREER awards for her research on equivariant topological field theories and higher cluster categories. Her recent publications explore combinatorial models, enriched categories, and homotopy limits in the context of functor calculus and higher structures. Julie Bergner contributes to mathematical exposition through articles on writing papers in the mathematical sciences and homotopy theory applications. She is actively involved in the department's topology seminar and supports collaborative learning initiatives. Her research has implications in algebraic topology, category theory, and their interdisciplinary applications.

• Homotopy Theory
• Algebraic Topology
• Algebraic K-Theory
• +3 more

Nathan (Nati) Linial is a Professor at the School of Computer Science and Engineering at the Hebrew University of Jerusalem, where he has been a faculty member since completing his postdoctoral period at UCLA. He earned his undergraduate degree in mathematics from the Technion and his PhD in graph theory from the Hebrew University. His research spans multiple areas of theoretical computer science and mathematics, with primary focus on combinatorics, theoretical computer science, and bioinformatics. Linial's work has made significant contributions to high-dimensional combinatorics, expander graphs, metric embeddings, and computational molecular biology. His research often bridges geometry, analysis, and combinatorial structures, demonstrating deep connections between seemingly disparate mathematical fields. Linial's recent publications reveal a strong trend toward high-dimensional combinatorial structures, including simplicial complexes, hypertrees, and high-dimensional permutations. His work frequently employs probabilistic methods, linear programming techniques, and geometric approaches to solve fundamental combinatorial problems. The breadth of his research is evident in both pure mathematical contributions and applications to computational biology. Fellow of the American Mathematical Society ISI Highly Cited Researcher Conant Prize (2008) for the influential survey paper "Expander graphs and their applications" Linial has served on the editorial boards of several prestigious journals including the Israel Journal of Mathematics (as Chief Editor 2013-2017), Random Structures and Algorithms, and Combinatorica. His academic leadership extends to organizing conferences and workshops in combinatorics and theoretical computer science. He has mentored numerous students whose work spans theoretical computer science, combinatorics, and computational biology. Linial is associated with research projects including ProtoNet (for protein sequence classification) and EVEREST (for evolutionary conserved protein domains), demonstrating his commitment to interdisciplinary research that bridges computer science with molecular biology.

• Combinatorics
• Theoretical Computer Science
• Bioinformatics
• +6 more

Michael Schaub is a tenure-track Assistant Professor in the Department of Computer Science at RWTH Aachen University, specializing in Computational Network Science. His research focuses on analyzing complex systems through network and graph models, integrating dynamical systems, control theory, and machine learning. He leads the Computational Network Science group, advancing methodologies for higher-order network models like simplicial complexes and hypergraphs. Schaub holds a PhD from Imperial College London and has held postdoctoral positions at MIT and Oxford. He is an ERC Starting Grant recipient (2022) and a Marie Curie Fellow, recognized for contributions to network dynamics and topological data analysis. Education: PhD in Mathematics, Imperial College London (2011-2015) MSc in Biomedical Engineering, Imperial College London (2010) BSc in Electrical Engineering, ETH Zurich (2007-2010) Research Interests: Schaub’s work spans interdisciplinary applications of network science, including biological systems, social networks, and technical infrastructures. Key areas include: Higher-order network models (hypergraphs, simplicial complexes) Graph signal processing and dynamics on networks Community detection and dynamical systems analysis Topological data analysis and machine learning Grants & Awards: ERC Starting Grant (2022): HIGH-HOPeS project Marie Skłodowska-Curie Fellowship (2017-2019) Junior Fellow, German Informatics Society (GI) Member of Junges Kolleg (North Rhine-Westphalia Academy) Labs & Teams: Leads the Computational Network Science Lab at RWTH Aachen, collaborating internationally on projects like the ELLIS Society and the European Laboratory for Learning and Intelligent Systems (ELLIS). Active in organizing workshops (e.g., Toponets, SIAM MDS).

• Network Science
• Dynamical Systems
• Machine Learning
• +3 more

Prof. Dmitri Krioukov is an Associate Professor in the Department of Physics at Northeastern University and holds an affiliated faculty position in Electrical and Computer Engineering. He directs the DK-Lab at the Network Science Institute, focusing on theoretical aspects of complex networks, including latent network geometry, random geometric graphs, and navigation in networks. His work bridges mathematical physics and applied network science, with applications to real-world data such as the Internet's structure. Research interests revolve around the interplay between network topology and geometry, including studies of causal sets, graph curvature, and dynamics in complex systems. He has pioneered frameworks linking network growth to hyperbolic geometry, enabling efficient routing algorithms. Notable contributions include the discovery of latent geometric structures underlying real-world networks and their implications for navigation and scalability. He has been recognized for high-impact publications, including multiple Stanford University Annual Assessments placing him among the top 2% most-cited scientists in his field (2024, 2023, 2022). His lab's interdisciplinary approach integrates principles from physics, mathematics, and computer science to address fundamental questions in network science.

• Network Science
• Complex Networks
• Mathematical Physics
• +7 more

Gijs Heuts is an Associate Professor in the Fundamental Mathematics group at the Mathematical Institute of Utrecht University, part of the Faculty of Science. His research focuses on advanced topics in algebraic topology and higher category theory, with particular expertise in Goodwillie calculus, chromatic homotopy theory, and operads. He is affiliated with the Utrecht Geometry Center, which includes prominent mathematicians Ieke Moerdijk and Lennart Meier. His work is currently funded by prestigious grants including an ERC Starting Grant titled "Chromatic homotopy theory of spaces" and an NWO Vidi grant "Hopf algebras and periodic homotopy theory". Starting September 2025, he will also serve as one of the Principal Investigators on the NWO XL consortium "Symmetry on the interface of topology and higher algebra". Dr. Heuts' research centers around homotopy theory and derived algebraic geometry, with a focus on generalizations of classical algebraic concepts (such as Lie algebras, commutative rings, and Hopf algebras) to homotopy theory. His work has significant applications to chromatic homotopy theory, with Goodwillie calculus and operads serving as central methodological tools. His publication record demonstrates consistent high-impact contributions to the field, with papers appearing in top journals such as Annals of Mathematics and Proceedings of the American Mathematical Society. His research spans theoretical foundations of higher category theory to specific applications in unstable homotopy theory, particularly focusing on connections between spectral Lie algebras and vn-periodic phenomena. ERC Starting Grant "Chromatic homotopy theory of spaces" NWO Vidi grant "Hopf algebras and periodic homotopy theory" PI on NWO XL consortium "Symmetry on the interface of topology and higher algebra" (starting Sept 2025) Dr. Heuts completed his PhD under Jacob Lurie at Harvard University and was previously a postdoc at the University of Copenhagen. He has held research positions at the Isaac Newton Institute and Hausdorff Research Institute. He was an organizer of the MIT Talbot Workshop (2012-2015) and currently organizes the European Autumn School in Topology (EAST).

• algebraic topology
• Goodwillie calculus
• chromatic homotopy theory
• +4 more

Christian Bick is an Associate Professor at the Department of Mathematics, Vrije Universiteit Amsterdam (VU Amsterdam). He holds visiting roles as a Visiting Research Fellow at the University of Oxford's Mathematical Institute, Honorary Associate Professor at the University of Exeter, and Visiting Fellow at the Institute for Advanced Study (TUM-IAS), Technische Universität München. His research focuses on dynamical systems and applications, particularly in network dynamics, coupled oscillator networks, and higher-order interactions. He has received prestigious awards such as the Marie Curie Intra-European Fellowship (2015) and the Hans Fischer Fellowship (2019). Education and Career: Bick obtained his PhD from Georg-August-Universität Göttingen (2012) and held postdoctoral positions at Rice University and the University of Exeter. His work bridges theoretical and applied mathematics, with interdisciplinary collaborations in neuroscience, physics, and engineering. Research Interests: Bick explores dynamics of coupled oscillator networks, asynchronous networks, and higher-order interactions. His recent work includes studies on heteroclinic networks, chimera states, and synchronization phenomena in complex systems. He leads projects like BeyondTheEdge (Marie Skłodowska–Curie Doctoral Network) and has contributed to grants such as the EPSRC New Investigator Award (2020–2023). Teaching: He teaches Dynamical Systems at VU Amsterdam and has lectured on Stochastic Processes, Mathematical Methods, and Dynamical Systems and Chaos at the University of Exeter and Oxford. Awards and Grants: His honors include the DAAD Doktorandenstipendien (2010, 2012) and Fulbright support (2008). Active grants include projects on higher-order networks and neurodegenerative disease modeling.

• Dynamical Systems
• Coupled Oscillator Networks
• Network Dynamics
• +3 more