Marcolli Matilde's Books

Noncommutative Cosmology

By: Matilde Marcolli

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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.

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292

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World Scientific

Published Date

ISBN 10

9813202866

ISBN 13

9789813202863

An Invitation to Noncommutative Geometry

By: Masoud Khalkhali,Matilde Marcolli

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An Invitation to Noncommutative Geometry

By: Masoud Khalkhali,Matilde Marcolli

This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory.

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515

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World Scientific

Published Date

ISBN 10

981270616X

ISBN 13

9789812706164

Lumen Naturae

Visions of the Abstract in Art and Mathematics

By: Matilde Marcolli

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Lumen Naturae

Visions of the Abstract in Art and Mathematics

By: Matilde Marcolli

Exploring common themes in modern art, mathematics, and science, including the concept of space, the notion of randomness, and the shape of the cosmos. This is a book about art—and a book about mathematics and physics. In Lumen Naturae (the title refers to a purely immanent, non-supernatural form of enlightenment), mathematical physicist Matilde Marcolli explores common themes in modern art and modern science—the concept of space, the notion of randomness, the shape of the cosmos, and other puzzles of the universe—while mapping convergences with the work of such artists as Paul Cezanne, Mark Rothko, Sol LeWitt, and Lee Krasner. Her account, focusing on questions she has investigated in her own scientific work, is illustrated by more than two hundred color images of artworks by modern and contemporary artists. Thus Marcolli finds in still life paintings broad and deep philosophical reflections on space and time, and connects notions of space in mathematics to works by Paul Klee, Salvador Dalí, and others. She considers the relation of entropy and art and how notions of entropy have been expressed by such artists as Hans Arp and Fernand Léger; and traces the evolution of randomness as a mode of artistic expression. She analyzes the relation between graphical illustration and scientific text, and offers her own watercolor-decorated mathematical notebooks. Throughout, she balances discussions of science with explorations of art, using one to inform the other. (She employs some formal notation, which can easily be skipped by general readers.) Marcolli is not simply explaining art to scientists and science to artists; she charts unexpected interdependencies that illuminate the universe.

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390

Publisher

MIT Press

Published Date

ISBN 10

0262043904

ISBN 13

9780262043908

Deformation Spaces

Perspectives on algebro-geometric moduli

By: Hossein Abbaspour,Matilde Marcolli,Thomas Tradler

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Deformation Spaces

Perspectives on algebro-geometric moduli

By: Hossein Abbaspour,Matilde Marcolli,Thomas Tradler

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.

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174

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3834896802

ISBN 13

9783834896803

Feynman Motives

By: Matilde Marcolli

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Feynman Motives

By: Matilde Marcolli

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. The main question is whether residues of Feynman integrals always evaluate to periods of mixed Tate motives, as appears to be the case from extensive computations of Feynman integrals carried out 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 grew out of work of Bloch–Esnault–Kreimer and suggests that, while the algebraic varieties associated to the Feynman graphs can be arbitrarily complicated as motives, the part 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 Connes and the author, consists of comparing a Tannakian category constructed out of the data of renormalization with those formed by mixed Tate motives. The book draws connections between these two approaches and gives an overview of various ongoing directions of research in the field. The text is aimed at researchers in mathematical physics, high energy physics, number theory and algebraic geometry. Based on lecture notes for a graduate course given by the author at Caltech in the fall of 2008, it cal also be used by graduate students interested in working in this area.

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234

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World Scientific

Published Date

ISBN 10

9814271209

ISBN 13

9789814271202

Lumen Naturae

Visions of Space in Art and Mathematics

By: Matilde Marcolli

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Lumen Naturae

Visions of Space in Art and Mathematics

By: Matilde Marcolli

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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Page Count

250

Publisher

Springer

Published Date

ISBN 10

3319130978

ISBN 13

9783319130972

Lumen Naturae

Visions of the Abstract in Art and Mathematics

By: Matilde Marcolli

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Lumen Naturae

Visions of the Abstract in Art and Mathematics

By: Matilde Marcolli

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390

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MIT Press

Published Date

ISBN 10

0262043904

ISBN 13

9780262043908

Deformation Spaces

Perspectives on algebro-geometric moduli

By: Hossein Abbaspour,Matilde Marcolli,Thomas Tradler

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Deformation Spaces

Perspectives on algebro-geometric moduli

By: Hossein Abbaspour,Matilde Marcolli,Thomas Tradler

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174

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Springer Science & Business Media

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ISBN 10

3834896802

ISBN 13

9783834896803

Noncommutative Geometry, Quantum Fields and Motives

By: Alain Connes,Matilde Marcolli

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Noncommutative Geometry, Quantum Fields and Motives

By: Alain Connes,Matilde Marcolli

The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.

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810

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470450453

ISBN 13

9781470450458

Noncommutative Cosmology

By: Matilde Marcolli

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Noncommutative Cosmology

By: Matilde Marcolli

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292

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World Scientific

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ISBN 10

9813202866

ISBN 13

9789813202863

Quantum Groups and Noncommutative Spaces

Perspectives on Quantum Geometry

By: Matilde Marcolli,Deepak Parashar

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Quantum Groups and Noncommutative Spaces

Perspectives on Quantum Geometry

By: Matilde Marcolli,Deepak Parashar

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.

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Page Count

240

Publisher

Vieweg+Teubner Verlag

Published Date

ISBN 10

3834814423

ISBN 13

9783834814425

Feynman Motives

By: Matilde Marcolli

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Feynman Motives

By: Matilde Marcolli

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Solve jigsaw puzzle

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Page Count

234

Publisher

World Scientific

Published Date

ISBN 10

9814271209

ISBN 13

9789814271202

Book's by Marcolli Matilde

Noncommutative Cosmology

Noncommutative Cosmology

An Invitation to Noncommutative Geometry

An Invitation to Noncommutative Geometry

Lumen Naturae

Lumen Naturae

Deformation Spaces

Deformation Spaces

Feynman Motives

Feynman Motives

Lumen Naturae

Lumen Naturae

Lumen Naturae

Lumen Naturae

Deformation Spaces

Deformation Spaces

Noncommutative Geometry, Quantum Fields and Motives

Noncommutative Geometry, Quantum Fields and Motives

Noncommutative Cosmology

Noncommutative Cosmology

Quantum Groups and Noncommutative Spaces

Quantum Groups and Noncommutative Spaces

Feynman Motives

Feynman Motives

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