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Showing 1 - 13 of 13 matches in All Departments

Deformation Spaces - Perspectives on Algebro-geometric Moduli (Hardcover, 2010): Hossein Abbaspour, Matilde Marcolli, Thomas... Deformation Spaces - Perspectives on Algebro-geometric Moduli (Hardcover, 2010)
Hossein Abbaspour, Matilde Marcolli, Thomas Tradler
R1,534 Discovery Miles 15 340 Ships in 10 - 15 working days

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 of Poisson algebras. They originate from activities at the Max-Planck-Institute for Mathematics and the Hausdorff Center for Mathematics in Bonn.

Quantum Groups and Noncommutative Spaces - Perspectives on Quantum Geometry (Hardcover, 2011 ed.): Matilde Marcolli, Deepak... Quantum Groups and Noncommutative Spaces - Perspectives on Quantum Geometry (Hardcover, 2011 ed.)
Matilde Marcolli, Deepak Parashar
R1,441 Discovery Miles 14 410 Ships in 10 - 15 working days

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.

Arithmetic and Geometry Around Quantization (Hardcover, 2010 ed.): OEzgur Ceyhan, Yu. I. Manin, Matilde Marcolli Arithmetic and Geometry Around Quantization (Hardcover, 2010 ed.)
OEzgur Ceyhan, Yu. I. Manin, Matilde Marcolli
R4,519 Discovery Miles 45 190 Ships in 10 - 15 working days

This volume comprises both research and survey articles originating from the conference on Arithmetic and Geometry around Quantization held in Istanbul in 2006. A wide range of topics related to quantization are covered, thus aiming to give a glimpse of a broad subject in very different perspectives.

Noncommutative Cosmology (Hardcover): Matilde Marcolli Noncommutative Cosmology (Hardcover)
Matilde Marcolli
R2,769 Discovery Miles 27 690 Ships in 10 - 15 working days

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. The book discusses applications to early universe models and slow-roll inflation models, to the problem of cosmic topology, to non-isotropic cosmologies like mixmaster universes and Bianchi IX gravitational instantons, and to multifractal structures in cosmology.Relations between noncommutative and algebro-geometric methods in cosmology is also discussed, including the occurrence of motives, periods, and modular forms in spectral models of gravity.

Noncommutative Cosmology (Paperback): Matilde Marcolli Noncommutative Cosmology (Paperback)
Matilde Marcolli
R1,344 Discovery Miles 13 440 Ships in 10 - 15 working days

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. The book discusses applications to early universe models and slow-roll inflation models, to the problem of cosmic topology, to non-isotropic cosmologies like mixmaster universes and Bianchi IX gravitational instantons, and to multifractal structures in cosmology.Relations between noncommutative and algebro-geometric methods in cosmology is also discussed, including the occurrence of motives, periods, and modular forms in spectral models of gravity.

Feynman Motives (Paperback): Matilde Marcolli Feynman Motives (Paperback)
Matilde Marcolli
R715 Discovery Miles 7 150 Ships in 12 - 19 working days

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 subject are described. The first, a "bottom-up" approach, constructs explicit algebraic varieties and periods from Feynman graphs and parametric Feynman integrals. This approach, which grew out of work of Bloch-Esnault-Kreimer and was more recently developed in joint work of Paolo Aluffi and the author, leads to algebro-geometric and motivic versions of the Feynman rules of quantum field theory and concentrates on explicit constructions of motives and classes in the Grothendieck ring of varieties associated to Feynman integrals. While the varieties obtained in this way can be arbitrarily complicated as motives, the part of the cohomology that is involved in the Feynman integral computation might still be of the special mixed Tate kind. A second, "top-down" approach to the problem, developed in the work of Alain Connes and the author, consists of comparing a Tannakian category constructed out of the data of renormalization of perturbative scalar field theories, obtained in the form of a Riemann-Hilbert correspondence, with Tannakian categories of mixed Tate motives. The book draws connections between these two approaches and gives an overview of other ongoing directions of research in the field, outlining the many connections of perturbative quantum field theory and renormalization to motives, singularity theory, Hodge structures, arithmetic geometry, supermanifolds, algebraic and non-commutative geometry.The text is aimed at researchers in mathematical physics, high energy physics, number theory and algebraic geometry. Partly based on lecture notes for a graduate course given by the author at Caltech in the fall of 2008, it can also be used by graduate students interested in working in this area.

Feynman Motives (Hardcover): Matilde Marcolli Feynman Motives (Hardcover)
Matilde Marcolli
R1,325 Discovery Miles 13 250 Ships in 12 - 19 working days

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 subject are described. The first, a "bottom-up" approach, constructs explicit algebraic varieties and periods from Feynman graphs and parametric Feynman integrals. This approach, which grew out of work of Bloch-Esnault-Kreimer and was more recently developed in joint work of Paolo Aluffi and the author, leads to algebro-geometric and motivic versions of the Feynman rules of quantum field theory and concentrates on explicit constructions of motives and classes in the Grothendieck ring of varieties associated to Feynman integrals. While the varieties obtained in this way can be arbitrarily complicated as motives, the part of the cohomology that is involved in the Feynman integral computation might still be of the special mixed Tate kind. A second, "top-down" approach to the problem, developed in the work of Alain Connes and the author, consists of comparing a Tannakian category constructed out of the data of renormalization of perturbative scalar field theories, obtained in the form of a Riemann-Hilbert correspondence, with Tannakian categories of mixed Tate motives. The book draws connections between these two approaches and gives an overview of other ongoing directions of research in the field, outlining the many connections of perturbative quantum field theory and renormalization to motives, singularity theory, Hodge structures, arithmetic geometry, supermanifolds, algebraic and non-commutative geometry.The text is aimed at researchers in mathematical physics, high energy physics, number theory and algebraic geometry. Partly based on lecture notes for a graduate course given by the author at Caltech in the fall of 2008, it can also be used by graduate students interested in working in this area.

Deformation Spaces - Perspectives on Algebro-Geometric Moduli (Paperback, 2010 ed.): Hossein Abbaspour, Matilde Marcolli,... Deformation Spaces - Perspectives on Algebro-Geometric Moduli (Paperback, 2010 ed.)
Hossein Abbaspour, Matilde Marcolli, Thomas Tradler
R1,495 Discovery Miles 14 950 Ships in 10 - 15 working days

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 of Poisson algebras. They originate from activities at the Max-Planck-Institute for Mathematics and the Hausdorff Center for Mathematics in Bonn.

Noncommutative Geometry and Number Theory - Where Arithmetic meets Geometry and Physics (Paperback, 2006 ed.): Caterina Consani Noncommutative Geometry and Number Theory - Where Arithmetic meets Geometry and Physics (Paperback, 2006 ed.)
Caterina Consani; Series edited by Klas Diederich; Edited by Matilde Marcolli
R2,174 Discovery Miles 21 740 Ships in 10 - 15 working days

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.

Quantum Groups and Noncommutative Spaces - Perspectives on Quantum Geometry (Paperback, 2011 ed.): Matilde Marcolli, Deepak... Quantum Groups and Noncommutative Spaces - Perspectives on Quantum Geometry (Paperback, 2011 ed.)
Matilde Marcolli, Deepak Parashar
R1,393 Discovery Miles 13 930 Ships in 10 - 15 working days

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.

Frobenius Manifolds - Quantum Cohomology and Singularities (Paperback, Softcover reprint of the original 1st ed. 2004): Claus... Frobenius Manifolds - Quantum Cohomology and Singularities (Paperback, Softcover reprint of the original 1st ed. 2004)
Claus Hertling, Matilde Marcolli; Series edited by Klas Diederich
R3,162 Discovery Miles 31 620 Ships in 10 - 15 working days

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.

Invitation To Noncommutative Geometry, An (Hardcover): Matilde Marcolli, Masoud Khalkhali Invitation To Noncommutative Geometry, An (Hardcover)
Matilde Marcolli, Masoud Khalkhali
R6,446 Discovery Miles 64 460 Ships in 12 - 19 working days

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

Lumen Naturae 2017 - Visions of Space in Art and Mathematics (Hardcover, 2017 ed.): Matilde Marcolli Lumen Naturae 2017 - Visions of Space in Art and Mathematics (Hardcover, 2017 ed.)
Matilde Marcolli
R2,315 Discovery Miles 23 150 Out of stock

Written by a scholar recognized for important and diverse contributions to mathematical physics, geometry and number theory, this book is a erudite and brilliantly original exploration of parallel developments in (mostly modern) art, mathematics, and physics through the study of topics such as the still-life genre, physical and artistic visions of nothingness, the mathematical concept of space, the geometry of prime numbers, particle physics and cosmology, and artistic and mathematical encounters with randomness. A final chapter shows how the language of art, especially surrealist and dadaist art, can help raise awareness and stimulate debate around some darker aspects of the mathematical profession and some of the psychological difficulties associated to the work of mathematical research. While the intended audience does not necessarily consist of readers with a scientific background, the book will be organized in such a way that it can be read at two different levels, with some chapters that require no prior knowledge of mathematics, and some others that explore more advanced material. All key mathematical notions will be introduced and explained.

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