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• Homotopy Theory
• Operads
• Tensor-triangular Geometry
• +3 more

Scott Balchin is a Lecturer at the School of Mathematics and Physics at Queen's University Belfast. His research sits at the intersection of homotopy theory, combinatorics, and category theory, with a focus on structures like N∞ operads, tensor-triangular geometry, and lattice theory in algebraic contexts. Research Interests Homotopy Theory Operads and Higher Structures Combinatorics in Algebraic Topology Tensor-triangular Geometry Model Categories and Lattice Theory Research Activity Recent work explores the combinatorial foundations of N∞ operads for finite groups, conjugacy-class-based bijections in homotopy theory, and rigidity phenomena in chromatic homotopy categories. His publications span journals like the Journal of Pure and Applied Algebra and European Journal of Combinatorics , often involving collaborations with researchers such as Emily MacBrough and Kyle Ormsby. Contact Email: s.balchin@qub.ac.uk

Martin GallauerView profile

Assistant Professor

• Algebraic Geometry
• Algebraic Topology
• Representation Theory
• +3 more

Martin Gallauer is an Assistant Professor at the Mathematics Institute, University of Warwick, specializing in algebraic topology, algebraic geometry, and representation theory. His research explores tensor-triangular geometry, motivic homotopy theory, and the structure of permutation modules. Education includes a PhD in Mathematics (2015), MA in Philosophy (2011), and MS in Mathematics (2011) from the University of Zurich. Research focuses on the interplay between homotopy theory and arithmetic geometry, with investigations into motivic cohomology, p-adic cohomology theories, and categorical structures in representation theory. Publications concentrate on advances in tensor-triangular geometry (patch-density, spectral classifications), motivic phenomena (Artin-Tate motives, monodromy operators), and foundational frameworks (six-functor formalisms, universal coefficient systems). Articles frequently employ derived categories, Galois representations, and homological techniques. Current PhD students include Yorick Fuhrmann, Pier Federico Pacchiarotti, and Daniel Roebuck, working on problems in chromatic homotopy theory and geometric representation theory.

Or BrookView profile

Associate Professor

• Competition Law and Policy
• Antitrust
• Regulation
• +3 more

Dr. Or Brook is an Associate Professor of Competition Law and Policy at the School of Law, University of Leeds, and Deputy Director of the Centre for Business Law and Practice. They hold interdisciplinary qualifications, including a PhD from the Amsterdam Centre for European Law and Governance, an LLM in European Competition Law from the University of Amsterdam, and degrees in Law and Economics from the Hebrew University of Jerusalem. Research focuses on international EU competition law, antitrust, and empirical legal methods. Notable projects include the Priority Setting Project (funded by ESRC) and a comprehensive study of judicial review in EU competition law. They co-edit the Research Handbook on Abuse of Dominance and lead the UK branch of ASCOLA, contributing to policy discussions through international collaborations. Education: PhD in Law, University of Amsterdam LLM in European Competition Law, University of Amsterdam LLB and BSc in Economics, Hebrew University of Jerusalem Research interests emphasize empirical analyses of legal texts, institutional enforcement practices, and competition law’s intersections with other regulatory frameworks. Recent monograph Non-Competition Interests in EU Antitrust Law (Cambridge UP, 2022) presents novel empirical data on public policy influences in EU competition enforcement. Key awards include the Michael Beverley Innovation Fellowship (associated member), supporting entrepreneurial academic initiatives. Their work bridges law and economics through interdisciplinary methods, advocating for empirical rigor in European legal scholarship.

• Lie algebras
• Hopf algebras
• Representation theory
• +2 more

Yuri Bazlov is a Lecturer in Pure Mathematics at The University of Manchester. His research focuses on Lie algebras, Hopf algebras, representation theory, reflection groups, and Coxeter groups. He holds a PhD in Mathematics from the Weizmann Institute of Science (2003), specializing in exterior powers of adjoint representations of semisimple Lie algebras. His work explores algebraic structures such as rational Cherednik algebras, braided doubles, and Nichols–Woronowicz algebras, with applications to Schubert calculus and noncommutative geometry. Recent projects include studies on cocycle twists, quantum Segre maps, and mystic reflection groups. Bazlov has contributed to foundational areas like Drinfeld modules, invariant polynomials, and Harish-Chandra isomorphisms for Clifford algebras. His research bridges abstract algebra with geometric and combinatorial methods, often involving reflection groups and their representations. He supervises PhD students in topics such as Lie algebra actions on noncommutative rings and is actively involved in the Digital Futures research beacon at The University of Manchester.

• Algebra
• Representation Theory
• Semigroup Theory
• +3 more

Marianne Johnson is a Senior Lecturer in the School of Mathematics at the University of Manchester. She is a core member of the tropical mathematics research group and collaborates with institutions including Birmingham, Queen Mary University of London, and Warwick through an LMS Joint Research Network. Her research focuses on algebra and combinatorics, including free Lie algebras, representation theory, semigroup theory, and tropical algebra/geometry. She has contributed to EPSRC-funded projects such as 'Multiplicative Structure of Tropical Matrix Algebra' and 'Modular Lie Powers and Applications,' and participated in the CICADA interdisciplinary project. Her research interests span a wide array of algebraic topics: free Lie algebras explore the structure of non-associative algebras, while representation theory examines how algebraic structures act on vector spaces. Semigroup theory and tropical algebra involve studying combinatorial and geometric properties of matrices and monoids over semirings. Recent work includes studies on plactic-like monoids, tropical matrix identities, and linear functions preserving Green's relations. Johnson has co-authored over 29 publications, with recent trends emphasizing tropical algebra's applications to geometric and algorithmic problems, such as tropical matrix groups and hyperplane arrangements. Her work bridges pure mathematics with interdisciplinary fields like computational dynamics and healthcare through collaborations like CICADA. Notable projects include analyzing upper triangular tropical matrices and exploring NP-completeness in gossip monoids. She has advised three research students and contributed to grants involving EPSRC-funded projects. Her affiliations include the Data Science Institute, Algebra research group, and Tropical Mathematics cluster at Manchester. Her work also intersects with Digital Futures initiatives, reflecting her commitment to advancing computational and theoretical mathematics.