Softcover ISBN: 978-1-4704-7361-7
Product Code: CONM/813
This volume contains the proceedings of the thematic program on “Quantum symmetries: Tensor categories, topological quantum field theories, and vertex algebras” held from October 10?November 4, 2022, at the Centre de Recherches Mathematiques, Montreal, Quebec, Canada.
Quantum symmetries is a rapidly expanding area in which tensor categories are applied to mathematical physics, in particular, to conformal and topological quantum field theories. These fields, in turn, connect to a huge variety of modern mathematics, including representation theory, vertex operator algebras, Hopf algebras, link and knot invariants, geometry, subfactors, combinatorics, and so much more.
The thematic program on quantum symmetries featured advanced lecture courses and research seminars by international leaders of their respective fields. This proceedings volume is centered on the active research of the area, but also includes an in-depth survey of one of the main topics, W
-algebras.
Jethro van Ekeren ? Affine W
-algebras
Justine Fasquel ? OPEs of rank two W
-algebras
Andrew Riesen ? Fusion rings acting on vertex operator algebras: First steps
Alissa Furet and Theo Johnson-Freyd ? Ground-state degeneracy of twisted sectors of Conway moonshine SCFT
Simon Lentner ? Combinatorial principles that enforce a group structure
Eric C. Rowell, Hannah Solomon and Qing Zhang ? On near-group centers and super-modular categories
Andrew Schopieray ? Fixed-point-free fusion automorphisms
Theo Johnson-Freyd ? (3+1)D
topological orders with only a Z2
-charged particle
Jurgen Fuchs, Gregor Schaumann, Christoph Schweigert and Simon Wood ? Grothendieck-Verdier duality in categories of bimodules and weak module functors
Christian Blanchet, Martin Palmer and Awais Shaukat ? Action of subgroups of the mapping class group on Heisenberg homologies
Daniel Berwick-Evans, Emily Cliff, Laura Murray, Apurva Nakade and Emma Phillips ? Flat principal 2-group bundles and flat string structures
Jin-Cheng Guu ? Categorical center of higher genera
Joseph Vulakh ? Twisted homogeneous racks over the alternating groups
Graduate students and research mathematicians interested in W
-algebras, tensor categories and their applications in representation theory, and mathematical physics.
Softcover ISBN: 978-1-4704-7362-4
Contemporary Mathematics Volume: 814; 2025; 264 pp
MSC: Primary 14; 16; 17; 18; 20
This volume contains the proceedings of the AMS Special Session on Quantum Groups, Hopf Algebras, and Applications (in memory of Professor Earl J. Taft), which was held from October 22?23, 2022, at the University of Utah, Salt Lake City, Utah.
Hopf algebras play a crucial role in many areas of mathematics, from finite groups to tensor categories, and allows researchers to make many connections between these subjects. Applications of Hopf algebras to low dimensional topology, topological quantum field theory, and condensed matter physics provide further motivation for the study of representations of Hopf algebras and their generalizations.
In memory of Earl Jay Taft, a pioneer of the theory of Hopf algebras, this volume collects research articles on Hopf algebras, quantum groups, and tensor categories contributed by prominent researchers. The articles in this volume manifest the diversity and richness of the subject and contain exciting new results which will certainly have applications to different areas of mathematics and physics.
Nicolas Andruskiewitsch and Hector Martin Pena Pollastri ? On the finite-dimensional representations of the double of the Jordan plane
Yan-Hong Bao, Dong-Xing Fu, Yu Ye and James J. Zhang ? 2-unitary operads of GK-dimension 3
Pavel Etingof, Dmitri Nikshych and Victor Ostrik ? On a necessary condition for unitary categorification of fusion rings
Shlomo Gelaki and Guillermo Sanmarco ? On finite group scheme-theoretical categories, I
Istvan Heckenberger and Katharina Schafer ? Left coideal subalgebras of Nichols algebras
Siu-Hung Ng and Xingting Wang ? On Hopf algebras of dimension pn
in characteristic p
Peter Schauenburg ? Categorical Morita equivalence of pointed fusion categories, and subgroups
Taiki Shibata and Ryota Wakao ? On classification of Hopf superalgebras of low dimension
Kenichi Shimizu ? Nakayama functor for coalgebras and a categorical perspective of the integral theory for Hopf algebras
David E. Radford ? The gamma function and a certain sequence of differences
Graduate students and research mathematicians interested in Hopf algebras, quantum groups, and tensor categories.
Softcover ISBN: 978-1-4704-6459-2
Proceedings of Symposia in Applied Mathematics Volume: 80;
2025; Estimated: 182 pp
MSC: Primary 91; 11; 97; 55
The spread of memes and misinformation on social media, political redistricting, gentrification in urban communities, pedestrian movement in crowds, and the dynamics of voters are among the many social phenomena that researchers investigate in the field of complex systems. In the study of complex social systems, there is often also societal relevance to improving our understanding of how individuals interact with each other and their environment, giving rise to collective group dynamics.
The mathematical and computational study of complex social systems relies on and motivates the development of methods in many topics, including mathematical modeling, data analysis, network science, and topology and geometry. This volume is a collection of diverse articles about complex social systems. This collection includes both (1) survey and tutorial articles that introduce complex social systems and methods to study them and (2) manuscripts with original research that highlight a variety of mathematical areas and applications.
This book introduces the study of complex social systems to a broad mathematical audience. It will particularly appeal to people who are interested in applied mathematics.
Alexandria Volkening ? A primer on data-driven modeling \@ifstar{}of complex social systems
A. Halev, K. Patel, N. Rodriguez, M. Tewari and L. Wong ? A model for wealth concentration: From a discrete system to a PDE
Mason A. Porter ? A non-expert’s introduction to data ethics for mathematicians
Swarup Dhar, Vanessa Massaro, Darakhshan Mir and Nathan C. Ryan ? Uncertainty in criminal justice algorithms: Simulation studies of the Pennsylvania Additive Classification Tool
Heather Z. Brooks ? A tutorial on networks of social systems: A mathematical modeling perspective
Michelle Feng ? Interpreting topology in the context of social science
Graduate students and researchers interested in applications of mathematics in social sciences.
Softcover ISBN: 978-1-4704-7920-6
Product Code: CAR/38
The Carus Mathematical Monographs Volume: 38;
2025; Estimated: 228 pp
MSC: Primary 37; 11
Ergodic theory is concerned with the measure-theoretic or statistical properties of a dynamical system. This book provides a conversational introduction to the topic, guiding the reader from the classical questions of measure theory to modern results such as the polynomial recurrence theorem. Applications to number theory and combinatorics enhance the exposition, while also presenting the utility of ergodic theory in other areas of research.
The book begins with an introduction to measure theory and the Lebesgue integral. After this, the key concepts of the subject are covered: measure-preserving transformations, ergodicity, and invariant measures. These chapters also cover classical results such as Poincare's recurrence theorem and Birkhoff’s ergodic theorem. The book ends with more advanced topics, such as mixing, entropy, and an appendix on the weak* topology. Each chapter ends with numerous exercises with a range of difficulty levels, including a handful of open problems.
An excellent resource for anyone wishing to learn about ergodic theory, the book only assumes prior exposure to proof-based mathematics. Familiarity with real analysis would be ideal but is not required.
Introduction to measure theory
The Lebesgue integral
Some limit theorems
Measure-preserving transformations
The Poincare recurrence theorem
Ergodicity
Invariant measures
Mixing
Multiple recurrence and Szemeredi’s theorem
Polynomial recurrence
Entropy
The weak* topology
Bibliography
Index
Graduate students and researchers interested in ergodic theory and applications, e.g., statistical properties of continued fraction expansions.
Hardback
ISBN 9781032946443
339 Pages 30 B/W Illustrations
Published March 4, 2025
This popular textbook provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space, with emphasis upon the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions.
Measure Theory and Fine Properties of Functions, Second Edition includes many interesting items working mathematical analysts need to know, but are rarely taught. Topics covered include a review of abstract measure theory, including Besicovitch’s covering theorem, Rademacher’s theorem (on the differentiability a.e. of Lipschitz continuous functions), the area and coarea formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Aleksandrov’s theorem (on the twice differentiability a.e. of convex functions).
The topics are carefully selected, and the proofs are succinct, but complete. This book provides ideal reading for mathematicians and graduate students in pure and applied mathematics. The authors assume readers are at least fairly conversant with both Lebesgue measure and abstract measure theory, and the expository style reflects this expectation. The book does not offer lengthy heuristics or motivation, but as compensation presents all the technicalities of the proofs.
This new Second Edition has been updated to provide corrections and minor edits from the previous Revised Edition, with countless improvements in notation, format and clarity of exposition. Also new is a section on the sub differentials of convex functions, and in addition the bibliography has been updated.
1 Measure Theory
2 Hausdorff Measures
3 Area and Coarea Formulas
4 Sobolev Functions
5 Functions of Bounded Variation, Sets of Finite Perimeter
6 Differentiability, Approximation by C1 Functions