Key Features - Emphasizes the interplay of analysis, differential and algebraic geometry, categorical constructions and physics in the context of noncommutative geometry - Conveniently divided into three sections: operator algebras and differential noncommutative geometry; categories and algebraic noncommutative geometry; and applications of noncommutative geometry to physics
Key Features - Emphasizes the interplay of analysis, differential and algebraic geometry, categorical constructions and physics in the context of n...
This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods. One of the main questions in the field is understanding when the residues of Feynman integrals in perturbative quantum field theory evaluate to periods of mixed Tate motives. The question originates from the occurrence of multiple zeta values in Feynman integrals calculations observed by Broadhurst and Kreimer.Two different approaches to the...
This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in pe...
This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods. One of the main questions in the field is understanding when the residues of Feynman integrals in perturbative quantum field theory evaluate to periods of mixed Tate motives. The question originates from the occurrence of multiple zeta values in Feynman integrals calculations observed by Broadhurst and Kreimer.Two different approaches to the...
This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in pe...
In recent decades, quantization has led to interesting applications in various mathematical branches. This volume, comprised of research and survey articles, discusses key topics, including symplectic and algebraic geometry, representation theory, quantum groups, the geometric Langlands program, quantum ergodicity, and non-commutative geometry. A wide range of topics related to quantization are covered, giving a glimpse of the broad subject. The articles are written by distinguished mathematicians in the field and reflect subsequent developments following the Arithmetic and Geometry around...
In recent decades, quantization has led to interesting applications in various mathematical branches. This volume, comprised of research and survey...
Abbaspour, Hossein Marcolli, Matilde Tradler, Thomas
The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since then, deformation theory has been applied as a useful tool in the study of many other mathematical structures, and even today it plays an important role in many developments of modern mathematics. This volume collects a few self-contained and peer-reviewed papers by experts which present up-to-date research topics in algebraic and motivic topology, quantum field theory, algebraic geometry, noncommutative geometry and the deformation theory...
The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since...
Quantum cohomology, the theory of Frobenius manifolds and the relations to integrable systems are flourishing areas since the early 90's. An activity was organized at the Max-Planck-Institute for Mathematics in Bonn, with the purpose of bringing together the main experts in these areas. This volume originates from this activity and presents the state of the art in the subject.
Quantum cohomology, the theory of Frobenius manifolds and the relations to integrable systems are flourishing areas since the early 90's. An activ...
The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since then, deformation theory has been applied as a useful tool in the study of many other mathematical structures, and even today it plays an important role in many developments of modern mathematics. This volume collects a few self-contained and peer-reviewed papers by experts which present up-to-date research topics in algebraic and motivic topology, quantum field theory, algebraic geometry, noncommutative geometry and the deformation theory...
The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since...
In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. Research across these ?elds has now reached an imp- tant turning point, as shows the increasing interest with which the mathematical community approaches these topics. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new c- nections between the ?elds of number theory, algebraic geometry and noncom- tative geometry....
In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical...
This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an acitvity at the Max-Planck-Institute for Mathematics in Bonn.
This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation th...
Modified gravity models play an important role in contemporary theoretical cosmology. The present book proposes a novel approach to the topic based on techniques from noncommutative geometry, especially the spectral action functional as a gravity model.
Modified gravity models play an important role in contemporary theoretical cosmology. The present book proposes a novel approach to the topic based on...
