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Noncommutative differential geometry is a novel approach to geometry that is paving the way for exciting new directions in the development of mathematics and physics. The contributions in this volume are based on papers presented at a workshop dedicated to enhancing international cooperation between mathematicians and physicists in various aspects of frontier research on noncommutative differential geometry. The active contributors present both the latest results and comprehensive reviews of topics in the area. The book is accessible to researchers and graduate students interested in a variety of mathematical areas related to noncommutative geometry and its interface with modern theoretical physics.
Noncommutative differential geometry is a novel approach to geometry, aimed in part at applications in physics. It was founded in the early eighties by the 1982 Fields Medalist Alain Connes on the basis of his fundamental works in operator algebras. It is now a very active branch of mathematics with actual and potential applications to a variety of domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field. It is an important topic both for mathematics and physics.
Noncommutative geometry is a novel approach which is opening up new possibilities for geometry from a mathematical viewpoint. It is also providing new tools for the investigation of quantum space-time in physics. Recent developments in string theory have supported the idea of quantum spaces, and have strongly stimulated the research in this field. This self-contained volume contains survey lectures and research articles which address these issues and related topics. The book is accessible to both researchers and graduate students beginning to study this subject.
Noncommutative differential geometry is a novel approach to geometry that is paving the way for exciting new directions in the development of mathematics and physics. The contributions in this volume are based on papers presented at a workshop dedicated to enhancing international cooperation between mathematicians and physicists in various aspects of frontier research on noncommutative differential geometry. The active contributors present both the latest results and comprehensive reviews of topics in the area. The book is accessible to researchers and graduate students interested in a variety of mathematical areas related to noncommutative geometry and its interface with modern theoretical physics.
Nonanticommutative harmonic superspace and N = 2 supersymmetric U(l) gauge theory / Takeo Araki, Katsushi Ito and Akihisa Ohtsuka -- Noncommutative locally anti-de sitter black holes / Pierre Bieliavsky ... [et al.] -- Dynamics of fuzzy spaces / M. Burić and John Madore -- Induction of representations in deformation quantization / Henrique Bursztyn and Stefan Waldmann -- [symbol]-function regularization and index theory in noncommutative geometry / Alexander Cardona -- Line bundles on fuzzy CP[symbol] / Ursula Carow-Watamura and Satoshi Watamura -- Construction of Lagrangian embeddings using Hamiltonian actions / River Chiang -- Deformation quantization of complex involutive submanifolds / Andrea D'Agnolo and Pietro Polesello -- Deformation quantization on a Hilbert space / Giuseppe Dito -- Symmetries and Moduli spaces of the self-dual Yang-Mills equations / James D. E. Grant -- Noncommutative solitons and integrable systems / Masashi Hamanaka -- On the connectedness of the spaces of surface group representations / Nan-Kuo Ho and Chiu-Chu Melissa Liu -- Witten's deformed Laplacian and its classical mechanics / Atsushi Inoue -- The vanishing problem for cohomology of superspaces / Daisuke Kato -- Higher dimensional spherical D-branes and matrix model / Yusuke Kimura -- Instantons of [symbol]-models in noncommutative geometry / Giovanni Landi -- On vectorial Gerbes and Poincaré-Cartan classes / Naoya Miyazaki -- A short note on symplectic Floer theory / Kaoru Ono -- Noncommutative cohomological field theories and topological aspects of matrix models / Akifumi Sako -- Gauge theory on fuzzy S[symbol] and CP[symbol] and random matrices / Harold Steinacker -- Relation on spin bundle Gerbes and Mayer's dirac operators / Atsushi Tomoda
Includes entries for maps and atlases.
This two-volume book presents an unusually diverse selection of research papers, covering all major topics in the fields of information and communication technologies and related sciences. It provides a wide-angle snapshot of current themes in information and power engineering, pursuing a cross-disciplinary approach to do so. The book gathers revised contributions that were presented at the 2018 International Conference: Sciences of Electronics, Technologies of Information and Telecommunication (SETIT'18), held on 20–22 December 2018 in Hammamet, Tunisia. This eighth installment of the event attracted a wealth of submissions, and the papers presented here were selected by a committee of experts and underwent additional, painstaking revision. Topics covered include: · Information Processing · Human-Machine Interaction · Computer Science · Telecommunications and Networks · Signal Processing · Electronics · Image and Video This broad-scoped approach is becoming increasingly popular in scientific publishing. Its aim is to encourage scholars and professionals to overcome disciplinary barriers, as demanded by current trends in the industry and in the consumer market, which are rapidly leading toward a convergence of data-driven applications, computation, telecommunication, and energy awareness. Given its coverage, the book will benefit graduate students, researchers and practitioners who need to keep up with the latest technological advances.
The Algorithmic Number Theory Symposium (ANTS), held biennially since 1994, is the premier international forum for research in computational and algorithmic number theory. ANTS is devoted to algorithmic aspects of number theory, including elementary, algebraic, and analytic number theory, the geometry of numbers, arithmetic algebraic geometry, the theory of finite fields, and cryptography.This volume is the proceedings of the fourteenth ANTS meeting, which took place 29 June to 4 July 2020 via video conference, the plans for holding it at the University of Auckland, New Zealand, having been disrupted by the COVID-19 pandemic. The volume contains revised and edited versions of 24 refereed papers and one invited paper presented at the conference.