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Quanta of Maths
The work of Alain Connes has cut a wide swath across several areas of mathematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics. Specific themes covered by the articles are as follows: entropy in operator algebras, regular $C^*$-algebras of integral domains, properly infinite $C^*$-algebras, representations of free groups and 1-cohomology, Leibniz seminorms and quantum metric spaces; von Neumann algebras, fundamental Group of $\mathrm{II}_1$ factors, subfacto...
Noncommutative Geometry and Number Theory
In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.
C*-algebras and Elliptic Theory
This book consists of reviewed original research papers and expository articles in index theory (especially on singular manifolds), topology of manifolds, operator and equivariant K-theory, Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others, and applications in mathematical physics. The wide spectrum of subjects reflects the diverse directions of research for which the starting point was the Atiyah-Singer index theorem.
K-theory and Noncommutative Geometry
Since its inception 50 years ago, K-theory has been a tool for understanding a wide-ranging family of mathematical structures and their invariants: topological spaces, rings, algebraic varieties and operator algebras are the dominant examples. The invariants range from characteristic classes in cohomology, determinants of matrices, Chow groups of varieties, as well as traces and indices of elliptic operators. Thus K-theory is notable for its connections with other branches of mathematics. Noncommutative geometry develops tools which allow one to think of noncommutative algebras in the same footing as commutative ones: as algebras of functions on (noncommutative) spaces. The algebras in quest...
Noncommutative Geometry and Physics 3
Noncommutative differential geometry has many actual and potential applications to several 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.
Proceedings of the 2nd Energy Security and Chemical Engineering Congress
This book presents selected articles presented at the 2nd Energy Security and Chemical Engineering Congress (ESChE 2021). This collection of proceedings presents the key challenges and trends related to mechanical as well as materials engineering and technology in setting the stage for promoting the sustainable technological solution for the better world. The book discusses recent explorations and findings with regard to mechanical and materials, specifically the thermal engineering and renewable energy areas that are very relevant toward the establishment of sustainable technological solutions. This book benefits academic researchers and industrial practitioners in the field of renewable energy and material engineering for energy applications.
Advances in Computation and Intelligence
Volumes CCIS 107 and LNCS 6382 constitute the proceedings of the 5th International Symposium, ISICA 2010, held in Wuhan, China, in October 2010. ISICA 2010 attracted 267 submissions and through rigorous reviews 53 papers were included in LNCS 6382. The papers are presented in sections on ANT colony and particle swarm optimization, differential evolution, distributed computing, genetic algorithms, multi-agent systems, multi-objective and dynamic optimization, robot intelligence, statistic learning and system design.
Noncommutative Geometry, Arithmetic, and Related Topics
Mathematics Institute, these essays collectively provide mathematicians and physicists with a comprehensive resource on the topic.
New Research on Genomic Instability
Many cancer biologists now believe that genomic instability not only initiates carcinogenesis, but also allows the tumour cell to become metastatic and evade drug toxicity. The loss of stability of the genome is becoming accepted as one of the most important aspects of carcinogenesis. One of the hallmarks of the cancer cell is the inherent instability of its genome. This book presents important research in this exciting field.
Topics in Cyclic Theory
This accessible introduction for Ph.D. students and non-specialists provides Quillen's unique development of cyclic theory.
