Marcolli, MatildeOverview
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Most widely held works by
Matilde Marcolli
Feynman motives
by Matilde Marcolli
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14 editions published between 2009 and 2010 in English and held by 1,069 WorldCat member libraries worldwide 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 "bottomup" approach, constructs explicit algebraic varieties and periods from Feynman graphs and parametric Feynman integrals. This approach, which grew out of work of BlochEsnaultKreimer and was more recently developed in joint work of Paolo Aluffi and the author, leads to algebrogeometric 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, "topdown" 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 RiemannHilbert 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 noncommutative 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
An invitation to noncommutative geometry
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13 editions published in 2008 in English and held by 876 WorldCat member libraries worldwide This is the only 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
Noncommutative geometry and number theory where arithmetic meets geometry and physics
by Caterina Consani
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10 editions published in 2006 in English and held by 449 WorldCat member libraries worldwide
Arithmetic and geometry around quantization
by Özgür Ceyhan
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13 editions published in 2010 in English and held by 446 WorldCat member libraries worldwide
Deformation spaces perspectives on algebrogeometric moduli
by Hossein Abbaspour
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10 editions published between 2002 and 2010 in English and held by 408 WorldCat member libraries worldwide
Quantum groups and noncommutative spaces perspectives on quantum geometry : a publication of the MaxPlanckInstitute for Mathematics, Bonn
by Matilde Marcolli
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13 editions published in 2011 in English and held by 404 WorldCat member libraries worldwide
Noncommutative geometry, quantum fields and motives
by Alain Connes
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10 editions published between 2007 and 2008 in English and held by 317 WorldCat member libraries worldwide "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 motive aspects come to play a role: spacetime, 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 longstanding problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces."BOOK JACKET
Arithmetic noncommutative geometry
by Matilde Marcolli
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7 editions published in 2005 in English and held by 207 WorldCat member libraries worldwide
Combinatorics and physics : MiniWorkshop on Renormalization, December 1516, 2006; Conference on Combinatorics and Physics, March 1923, 2007, Max Planck Institut für Mathematik, Bonn, Germany
by MiniWorkshop on Renormalization
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11 editions published in 2011 in English and held by 145 WorldCat member libraries worldwide
SeibergWitten gauge theory
by Matilde Marcolli
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10 editions published between 1990 and 2011 in English and held by 129 WorldCat member libraries worldwide
Frobenius manifolds : quantum cohomology and singularities : a publication of the MaxPlanckInstitute for Mathematics, Bonn
by Klaus Hertling
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4 editions published in 2004 in English and held by 119 WorldCat member libraries worldwide Frobenius manifolds are complex manifolds with a multiplication and a metric on the holomorphic tangent bundle, which satisfy several natural conditions. This notion was defined in 1991 by Dubrovin, motivated by physics results. Another source of Frobenius manifolds is singularity theory. Duality between string theories lies behind the phenomenon of mirror symmetry. One mathematical formulation can be given in terms of the isomorphism of certain Frobenius manifolds. A third source of Frobenius manifolds is given by integrable systems, more precisely, bihamiltonian hierarchies of evolutionary PDE's. As in the case of quantum cohomology, here Frobenius manifolds are part of an a priori much richer structure, which, because of strong constraints, can be determined implicitly by the underlying Frobenius manifolds. 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 MaxPlanckInstitute for Mathematics in 2002, 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
An invitation to noncommutative geometry : [lecture series given at the International Workshop on Noncommutative Geometry that took place at the Institute for Studies in Theoretical Physics and Mathematics (IPM) in Tehran in 2005, September 11  22]
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1 edition published in 2008 in English and held by 7 WorldCat member libraries worldwide
Quantum Groups and Noncommutative Spaces : Perspectives on Quantum Geometry ; [the present volume is based on an activity organized at the Max Planck Institute for Mathematics in Bonn, during the days August 68, 2007, dedicated to the topic of Quantum Groups and Noncommutative Geometry]
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1 edition published in 2011 in English and held by 7 WorldCat member libraries worldwide
Quantum groups and noncommutative spaces : perspectives on quantum geometry ; [An activity organized at the MaxPlanckInstitute for Mathematics in Bonn during the days August 68, 2007]
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1 edition published in 2011 in English and held by 5 WorldCat member libraries worldwide
Some remarks on conjugacy classes of bundle gauge groups
by Matilde Marcolli
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2 editions published in 1994 in English and held by 4 WorldCat member libraries worldwide
Holography principle and raithmetic of algebraic curves
by Yuri I Manin
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2 editions published in 2002 in English and held by 3 WorldCat member libraries worldwide
On the distribution of continued fractions and modular symbols
by Yuri I Manin
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2 editions published in 2001 in English and held by 3 WorldCat member libraries worldwide
Limiting modular symbols and the Lyapunov spectrum
by Matilde Marcolli
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2 editions published in 2001 in English and held by 3 WorldCat member libraries worldwide
Weak UCP and perturbed monopole equations
by B BoossBavnbrk
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3 editions published in 2002 in English and held by 3 WorldCat member libraries worldwide
A system of ODE for ASD connections and Dirac monopoles
by Matilde Marcolli
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2 editions published in 2002 in Russian and held by 3 WorldCat member libraries worldwide more
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Algebra Algebraic stacks Feynman integrals Frobenius algebras Frobenius manifolds Gauge fields (Physics) Geometric quantization Geometry Geometry, Algebraic Homology theory Manifolds (Mathematics) Mathematical physics Mathematics Moduli theory Motives (Mathematics) Noncommutative differential geometry Number theory Numerical integration Quantum field theory Quantum groups Quantum theory Renormalization group SeibergWitten invariants Singularities (Mathematics) Symplectic manifolds

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