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Billy WoodsView profile

Lecturer

• Algebra
• Ring Theory
• Noncommutative Algebra
• +3 more

Dr Billy Woods is a Lecturer in the Essex Pathways department at the University of Essex. His research focuses on algebraic structures, particularly in the areas of ring theory, noncommutative algebra, and Iwasawa algebras. He is actively involved in teaching, including courses such as Mathematical Methods and Statistics (IA115) and Mathematics for Computer Science (IA126). His work explores topics such as skew derivations, prime ideals in Iwasawa algebras, and the structure of p-adic analytic groups. Woods has published extensively in journals like the Israel Journal of Mathematics and Journal of Pure and Applied Algebra. His research contributes to foundational questions in noncommutative algebra and group theory. He is contactable at billy.woods@essex.ac.uk and located in room 4.118 at the Colchester Campus. Key research interests include dimensional analysis of skew power series rings, properties of virtually nilpotent groups, and homomorphic images in mod-p Iwasawa algebras. His recent work (2023-2025) emphasizes filtered skew derivations and bounded ring extensions, reflecting a focus on advancing theoretical algebraic frameworks. Previous studies (2016-2020) addressed catenarity in Iwasawa algebras and fixed rings in group ring quotients. His publications consistently address structural properties of noncommutative rings and their applications to group theory, with a particular emphasis on p-adic contexts. These contributions highlight interdisciplinary connections between algebraic structures and number theory.

Karol KoziolView profile

Assistant Professor

• Representation Theory
• Langlands Program
• p-adic Reductive Groups
• +4 more

Karol Koziol is an Assistant Professor in the Mathematics Department at Baruch College, City University of New York (CUNY), where his office is located in the Newman Vertical Campus. His research focuses on various aspects of the (local) Langlands Program, specifically representation theory of p-adic reductive groups, associated Hecke algebras, and Galois representations. His work is partially supported by NSF grant DMS-2310225. Dr. Koziol's academic journey includes: Ph.D. from Columbia University under Rachel Ollivier Undergraduate degree from NYU NSF Postdoctoral Fellowship at University of Toronto with Florian Herzig EPDI Postdoctoral Fellowship at Institut des Hautes Études Scientifiques and Max Planck Institute Postdoctoral positions at University of Michigan and University of Alberta His research bridges algebra, number theory, and representation theory with significant contributions to understanding modular representations of p-adic groups. Dr. Koziol's work examines supersingular representations, Hecke module structures, and cohomological aspects of representation theory in characteristic p, advancing knowledge in the modular local Langlands correspondence. Analysis of his publications reveals consistent focus on representation theory of p-adic groups across multiple dimensions: structural properties of Hecke algebras, cohomological behavior of representations, classification problems for specific group types, and connections to broader Langlands program objectives. His collaborative work with leading mathematicians demonstrates strong integration within the international research community. As an educator, Dr. Koziol teaches Elementary Probability (Math 3120) and Graph Theory (Math 4140) at Baruch College. He has mentored multiple undergraduate researchers through REU programs on topics including modular representations of division algebras and quaternion algebras, often collaborating with other prominent mathematicians like Tasho Kaletha and Charlotte Chan. Dr. Koziol actively contributes to the mathematical community through organizational roles including: Co-organizing the Baruch Distinguished Lecture Series Co-founding the CARTOON (Cross Atlantic Representation Theory and Other topics ONline) conference Participating in POINT: New Developments in Number Theory Contributing to MANTIS 2021 and other specialized workshops Preparing materials for the 2025 Arizona Winter School

Edward FrenkelView profile

Professor

• Representation Theory
• Algebraic Geometry
• Integrable Systems
• +2 more

Edward Frenkel is a Professor of Mathematics at the University of California, Berkeley since 1997. He previously served on the faculty at Harvard University and is renowned for his work at the intersection of Representation Theory , Algebraic Geometry , and Mathematical Physics , particularly the Langlands Program , which he describes as a Grand Unified Theory of mathematics. A member of the American Academy of Arts and Sciences and Fellow of the American Mathematical Society , he has received the Hermann Weyl Prize and the Euler Book Prize for his influential work. His research spans integrable systems , quantum duality , and mirror symmetry , with notable publications such as Langlands Correspondence for Loop Groups (2007) and Vertex Algebras and Algebraic Curves (2004, co-authored with D. Ben-Zvi). He has mentored PhD students including Xiwen Zhu (2009), Peter Pribik (2004), and Matthew Szczesny (2002). Frenkel’s public outreach includes his New York Times bestseller Love and Math , over 100 scholarly articles, and popular YouTube lectures amassing millions of views. His critical perspectives on algorithmic ethics, financial modeling, and education reform have sparked global discourse.

Shrawan KumarView profile

Professor

• Representation Theory
• Algebraic Geometry
• Lie Algebras
• +5 more

Shrawan Kumar is the J.R. & L.S. Parker Distinguished Professor in the Department of Mathematics at the University of North Carolina at Chapel Hill. He joined UNC in 1991 and has held the distinguished professorship since 2010. Additionally, he maintains an adjunct position at the Tata Institute of Fundamental Research (2006–present). His academic journey includes a B.Sc. from Gorakhpur University (1973), an M.Sc. from Bombay University (1975), and a Ph.D. from Bombay University (1986) under the supervision of S. Ramanan. Kumar's research centers on representation theory, algebraic geometry, and topology, with a focus on semisimple groups, Kac-Moody algebras, and their flag varieties. He investigates moduli spaces of principal bundles, eigenvalue problems, and geometric structures in representation theory. Key areas include Frobenius splitting, tensor product decompositions, and conformal blocks, blending algebraic, geometric, and combinatorial methods. His recent publications (2020–2025) demonstrate sustained engagement with representation theory, Kac-Moody algebras, and algebraic geometry. Trends include advances in equivariant K-theory, conformal field theory generalizations, combinatorial counterexamples, and homological structures in Lie theory. Works frequently intersect mathematical physics, showcasing applications in quantum algebra and vertex operator algebras.

• Operator Algebras
• Quantum Groups
• Functional Analysis
• +1 more

Reiji Tomatsu is a Professor at Hokkaido University’s Faculty of Education and Integrated Arts and Sciences , specializing in Operator Algebras and Quantum Groups . His research focuses on the structural analysis of von Neumann algebras and their interactions with quantum symmetries. Education: PhD in Mathematical Sciences from the University of Tokyo. Research Interests revolve around quantum group actions, Rohlin flows, Haagerup approximation properties, and classification of operator algebras. He investigates infinite tensor product actions, coideals, and modular invariants, often leveraging functional analysis and mathematical physics frameworks. His recent publications emphasize quantum group dynamics and von Neumann algebra structures , including classification theorems for coideal $C^*$-algebras and fullness of type III factors. These works intersect with noncommutative geometry and representation theory. Grants: He has continuously received Japan Society for the Promotion of Science (JSPS) research grants since 2007, advancing studies on quantum group actions and operator algebraic symmetries. Teaching: Tomatsu delivers graduate-level courses in analysis, Fourier analysis, and mathematics education at Hokkaido University’s Graduate School of Education.

• Arithmetic Geometry
• Coding Theory
• Galois Representations
• +3 more

Jérémy Le Borgne is an Assistant Professor in the Department of Mathematics at ENS Rennes, where he has held faculty positions since 2012. He is a core member of IRMAR's Geometry and Effective Algebra Team, contributing to France's national mathematics research infrastructure through this CNRS-affiliated institute. His dual role encompasses advanced teaching from undergraduate to Agrégation levels and active research at the intersection of algebra, geometry, and computation. His educational foundation includes: ENS Cachan - Antenne de Bretagne (2005-2009) PhD in Mathematics, University of Rennes 1 (2009-2012), supervised by Xavier Caruso and David Lubicz Le Borgne's research pioneers computational approaches to arithmetic geometry, with seminal work on Ore polynomials enabling breakthroughs in Gabidulin code construction for error correction. His investigations into p-adic Galois representations bridge number theory and algorithm design, while recent studies of Hall bases for free Lie algebras reveal deep combinatorial structures applicable to differential equations. This tripartite focus creates synergies between theoretical mathematics and practical computation. Analysis of his 2010-2023 publications reveals consistent progression from foundational number theory (Ax-Sen-Tate theorem optimization) toward increasingly computational work, with 2022-2023 papers emphasizing algorithmic Lie algebra structures and nonlinear system expansions. His research demonstrates strong continuity in non-commutative algebra applications while expanding into new combinatorial territories. No formal awards are documented in public materials, though his publication record in high-impact journals like Journal of Algebra and Comptes Rendus Mathématique indicates peer recognition. His teaching portfolio spans advanced algebra courses and Agrégation preparation, with documented outreach including Lebesgue lectures and Olympiad training. As a research supervisor, Le Borgne integrates students through IRMAR's collaborative environment, though specific advisee counts aren't public. His Geometry and Effective Algebra Team provides infrastructure for computational mathematics projects, with recent work suggesting active funding for skew polynomial and Lie algebra research. The lab maintains close ties with University of Rennes 1's mathematics department, facilitating resource sharing across Rennes' academic ecosystem.