Marcolli, MatildeOverview
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Most widely held works by
Matilde Marcolli
Feynman motives
by Matilde Marcolli
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15 editions published between 2009 and 2010 in English and held by 1,204 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 subje
An invitation to noncommutative geometry
by Masoud Khalkhali
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14 editions published in 2008 in English and held by 1,100 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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12 editions published in 2006 in English and held by 451 WorldCat member libraries worldwide In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and KTheory. This volume collects and presents uptodate 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 padic groups, Shimura varieties, the local Lfactors 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
Arithmetic and geometry around quantization
by Özgür Ceyhan
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15 editions published in 2010 in English and held by 440 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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16 editions published in 2011 in English and held by 406 WorldCat member libraries worldwide
Noncommutative geometry, quantum fields and motives
by Alain Connes
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11 editions published between 2007 and 2008 in English and held by 320 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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8 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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13 editions published in 2011 in English and held by 150 WorldCat member libraries worldwide
SeibergWitten gauge theory
by Matilde Marcolli
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11 editions published between 1990 and 2011 in English and held by 130 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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5 editions published in 2004 in English and held by 128 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
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
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 Bernhelm Booss
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2 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
Lectures on arithmetic noncommutative geometry
by Matilde Marcolli
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2 editions published in 2004 in English and held by 2 WorldCat member libraries worldwide
Threedimensional aspects of SeibergWitten gauge theory
by Matilde Marcolli
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1 edition published in 1997 in English and held by 2 WorldCat member libraries worldwide
On reconstruction theorems in noncommutative Riemannian geometry
by Branimir Josip Cacic
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2 editions published in 2013 in English and held by 2 WorldCat member libraries worldwide
Solvmanifolds and noncommutative tori with real multiplication
by Matilde Marcolli
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2 editions published in 2007 in English and held by 2 WorldCat member libraries worldwide
On the distribution of continued fractions and modular symbols
by I︠U︡. I Manin
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1 edition published in 2001 in English and held by 2 WorldCat member libraries worldwide more
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Algebra Algebraic stacks Dirac equation Feynman integrals Frobenius algebras Frobenius manifolds Gauge fields (Physics) Geometric quantization Geometry Geometry, Algebraic Geometry, Riemannian 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 Threemanifolds (Topology)

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