WorldCat Identities

Marcolli, Matilde

Overview
Works: 71 works in 213 publications in 2 languages and 4,685 library holdings
Genres: Conference proceedings 
Roles: Editor, Thesis advisor
Classifications: QC174.17.F45, 512.55
Publication Timeline
Key
Publications about  Matilde Marcolli Publications about Matilde Marcolli
Publications by  Matilde Marcolli Publications by Matilde Marcolli
Most widely held works by Matilde Marcolli
Feynman motives by Matilde Marcolli ( )
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 "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
An invitation to noncommutative geometry ( )
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 ( )
10 editions published in 2006 in English and held by 449 WorldCat member libraries worldwide
Arithmetic and geometry around quantization by Özgür Ceyhan ( )
13 editions published in 2010 in English and held by 446 WorldCat member libraries worldwide
Deformation spaces perspectives on algebro-geometric moduli by Hossein Abbaspour ( )
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 Max-Planck-Institute for Mathematics, Bonn by Matilde Marcolli ( )
13 editions published in 2011 in English and held by 404 WorldCat member libraries worldwide
Noncommutative geometry, quantum fields and motives by Alain Connes ( Book )
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 inter-play 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: 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."--BOOK JACKET
Arithmetic noncommutative geometry by Matilde Marcolli ( Book )
7 editions published in 2005 in English and held by 207 WorldCat member libraries worldwide
Combinatorics and physics : Mini-Workshop on Renormalization, December 15-16, 2006; Conference on Combinatorics and Physics, March 19-23, 2007, Max Planck Institut für Mathematik, Bonn, Germany by Mini-Workshop on Renormalization ( Book )
11 editions published in 2011 in English and held by 145 WorldCat member libraries worldwide
Seiberg-Witten gauge theory by Matilde Marcolli ( Book )
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 Max-Planck-Institute for Mathematics, Bonn by Klaus Hertling ( Book )
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 Max-Planck-Institute 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 ( Book )
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 ( Book )
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 ( Book )
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 ( Book )
2 editions published in 2001 in English and held by 3 WorldCat member libraries worldwide
Weak UCP and perturbed monopole equations by B Booss-Bavnbrk ( Book )
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 ( Book )
2 editions published in 2002 in Russian and held by 3 WorldCat member libraries worldwide
 
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Languages
English (129)
Russian (2)
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