Cyclic Cohomology at 40: Achievements and Future Prospects - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Cyclic Cohomology at 40: Achievements and Future Prospects write by A. Connes. This book was released on 2023-02-23. Cyclic Cohomology at 40: Achievements and Future Prospects available in PDF, EPUB and Kindle. This volume contains the proceedings of the virtual conference on Cyclic Cohomology at 40: Achievements and Future Prospects, held from September 27–October 1, 2021 and hosted by the Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada. Cyclic cohomology, since its discovery forty years ago in noncommutative differential geometry, has become a fundamental mathematical tool with applications in domains as diverse as analysis, algebraic K-theory, algebraic geometry, arithmetic geometry, solid state physics and quantum field theory. The reader will find survey articles providing a user-friendly introduction to applications of cyclic cohomology in such areas as higher categorical algebra, Hopf algebra symmetries, de Rham-Witt complex, quantum physics, etc., in which cyclic homology plays the role of a unifying theme. The researcher will find frontier research articles in which the cyclic theory provides a computational tool of great relevance. In particular, in analysis cyclic cohomology index formulas capture the higher invariants of manifolds, where the group symmetries are extended to Hopf algebra actions, and where Lie algebra cohomology is greatly extended to the cyclic cohomology of Hopf algebras which becomes the natural receptacle for characteristic classes. In algebraic topology the cyclotomic structure obtained using the cyclic subgroups of the circle action on topological Hochschild homology gives rise to remarkably significant arithmetic structures intimately related to crystalline cohomology through the de Rham-Witt complex, Fontaine's theory and the Fargues-Fontaine curve.
Categorical, Combinatorial and Geometric Representation Theory and Related Topics
Categorical, Combinatorial and Geometric Representation Theory and Related Topics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Categorical, Combinatorial and Geometric Representation Theory and Related Topics write by Pramod N. Achar. This book was released on 2024-07-11. Categorical, Combinatorial and Geometric Representation Theory and Related Topics available in PDF, EPUB and Kindle. This book is the third Proceedings of the Southeastern Lie Theory Workshop Series covering years 2015–21. During this time five workshops on different aspects of Lie theory were held at North Carolina State University in October 2015; University of Virginia in May 2016; University of Georgia in June 2018; Louisiana State University in May 2019; and College of Charleston in October 2021. Some of the articles by experts in the field describe recent developments while others include new results in categorical, combinatorial, and geometric representation theory of algebraic groups, Lie (super) algebras, and quantum groups, as well as on some related topics. The survey articles will be beneficial to junior researchers. This book will be useful to any researcher working in Lie theory and related areas.
String-Math 2022
String-Math 2022 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook String-Math 2022 write by Ron Donagi. This book was released on 2024-04-18. String-Math 2022 available in PDF, EPUB and Kindle. This is a proceedings volume from the String-Math conference which took place at the University of Warsaw in 2022. This 12th String-Math conference focused on several research areas actively developing these days. They included generalized (categorical) symmetries in quantum field theory and their relation to topological phases of matter; formal aspects of quantum field theory, in particular twisted holography; various developments in supersymmetric gauge theories, BPS counting and Donaldson–Thomas invariants. Other topics discussed at this conference included new advances in Gromov–Witten theory, curve counting, and Calabi–Yau manifolds. Another broad topic concerned algebraic aspects of conformal field theory, vertex operator algebras, and quantum groups. Furthermore, several other recent developments were presented during the conference, such as understanding the role of operator algebras in the presence of gravity, derivation of gauge-string duality, complexity of black holes, or mathematical aspects of the amplituhedron. This proceedings volume contains articles summarizing 14 conference lectures, devoted to the above topics.
Frontiers in Geometry and Topology
Frontiers in Geometry and Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Frontiers in Geometry and Topology write by Paul M. N. Feehan. This book was released on 2024-07-19. Frontiers in Geometry and Topology available in PDF, EPUB and Kindle. This volume contains the proceedings of the summer school and research conference “Frontiers in Geometry and Topology”, celebrating the sixtieth birthday of Tomasz Mrowka, which was held from August 1–12, 2022, at the Abdus Salam International Centre for Theoretical Physics (ICTP). The summer school featured ten lecturers and the research conference featured twenty-three speakers covering a range of topics. A common thread, reflecting Mrowka's own work, was the rich interplay among the fields of analysis, geometry, and topology. Articles in this volume cover topics including knot theory; the topology of three and four-dimensional manifolds; instanton, monopole, and Heegaard Floer homologies; Khovanov homology; and pseudoholomorphic curve theory.
Computational Homology
Computational Homology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computational Homology write by Tomasz Kaczynski. This book was released on 2006-04-18. Computational Homology available in PDF, EPUB and Kindle. Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.
