Marcolli, Matilde
Overview
Works:  93 works in 293 publications in 2 languages and 6,887 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other, Thesis advisor 
Classifications:  QA641, 512.55 
Publication Timeline
.
Most widely held works by
Matilde Marcolli
Feynman motives by
Matilde Marcolli(
)
21 editions published between 2009 and 2010 in English and held by 1,781 WorldCat member libraries worldwide
1. Perturbative quantum field theory and Feynman diagrams. 1.1. A calculus exercise in Feynman integrals. 1.2. From Lagrangian to effective action. 1.3. Feynman rules. 1.4. Simplifying graphs : vacuum bubbles, connected graphs. 1.5. Oneparticleirreducible graphs. 1.6. The problem of renormalization. 1.7. Gamma functions, Schwinger and Feynman parameters. 1.8. Dimensional regularization and minimal subtraction  2. Motives and periods. 2.1. The idea of motives. 2.2. Pure motives. 2.3. Mixed motives and triangulated categories. 2.4. Motivic sheaves. 2.5. The Grothendieck ring of motives. 2.6. Tate motives. 2.7. The algebra of periods. 2.8. Mixed Tate motives and the logarithmic extensions. 2.9. Categories and Galois groups. 2.10. Motivic Galois groups  3. Feynman integrals and algebraic varieties. 3.1. The parametric Feynman integrals. 3.2. The graph hypersurfaces. 3.3. Landau varieties. 3.4. Integrals in affine and projective spaces. 3.5. Nonisolated singularities. 3.6. Cremona transformation and dual graphs. 3.7. Classes in the Grothendieck ring. 3.8. Motivic Feynman rules. 3.9. Characteristic classes and Feynman rules. 3.10. Deletioncontraction relation. 3.11. Feynman integrals and periods. 3.12. The mixed Tate mystery. 3.13. From graph hypersurfaces to determinant hypersurfaces. 3.14. Handling divergences. 3.15. Motivic zeta functions and motivic Feynman rules  4. Feynman integrals and GelfandLeray forms. 4.1. Oscillatory integrals. 4.2. Leray regularization of Feynman integrals  5. ConnesKreimer theory in a nutshell. 5.1. The Bogolyubov recursion. 5.2. Hopf algebras and affine group schemes. 5.3. The ConnesKreimer Hopf algebra. 5.4. Birkhoff factorization. 5.5. Factorization and RotaBaxter algebras. 5.6. Motivic Feynman rules and RotaBaxter structure  6. The RiemannHilbert correspondence. 6.1. From divergences to iterated integrals. 6.2. From iterated integrals to differential systems. 6.3. Flat equisingular connections and vector bundles. 6.4. The "cosmic Galois group"7. The geometry of DimReg. 7.1. The motivic geometry of DimReg. 7.2. The noncommutative geometry of DimReg  8. Renormalization, singularities, and Hodge structures. 8.1. Projective radon transform. 8.2. The polar filtration and the Milnor fiber. 8.3. DimReg and mixed Hodge structures. 8.4. Regular and irregular singular connections  9. Beyond scalar theories. 9.1. Supermanifolds. 9.2. Parametric Feynman integrals and supermanifolds. 9.3. Graph supermanifolds. 9.4. Noncommutative field theories
21 editions published between 2009 and 2010 in English and held by 1,781 WorldCat member libraries worldwide
1. Perturbative quantum field theory and Feynman diagrams. 1.1. A calculus exercise in Feynman integrals. 1.2. From Lagrangian to effective action. 1.3. Feynman rules. 1.4. Simplifying graphs : vacuum bubbles, connected graphs. 1.5. Oneparticleirreducible graphs. 1.6. The problem of renormalization. 1.7. Gamma functions, Schwinger and Feynman parameters. 1.8. Dimensional regularization and minimal subtraction  2. Motives and periods. 2.1. The idea of motives. 2.2. Pure motives. 2.3. Mixed motives and triangulated categories. 2.4. Motivic sheaves. 2.5. The Grothendieck ring of motives. 2.6. Tate motives. 2.7. The algebra of periods. 2.8. Mixed Tate motives and the logarithmic extensions. 2.9. Categories and Galois groups. 2.10. Motivic Galois groups  3. Feynman integrals and algebraic varieties. 3.1. The parametric Feynman integrals. 3.2. The graph hypersurfaces. 3.3. Landau varieties. 3.4. Integrals in affine and projective spaces. 3.5. Nonisolated singularities. 3.6. Cremona transformation and dual graphs. 3.7. Classes in the Grothendieck ring. 3.8. Motivic Feynman rules. 3.9. Characteristic classes and Feynman rules. 3.10. Deletioncontraction relation. 3.11. Feynman integrals and periods. 3.12. The mixed Tate mystery. 3.13. From graph hypersurfaces to determinant hypersurfaces. 3.14. Handling divergences. 3.15. Motivic zeta functions and motivic Feynman rules  4. Feynman integrals and GelfandLeray forms. 4.1. Oscillatory integrals. 4.2. Leray regularization of Feynman integrals  5. ConnesKreimer theory in a nutshell. 5.1. The Bogolyubov recursion. 5.2. Hopf algebras and affine group schemes. 5.3. The ConnesKreimer Hopf algebra. 5.4. Birkhoff factorization. 5.5. Factorization and RotaBaxter algebras. 5.6. Motivic Feynman rules and RotaBaxter structure  6. The RiemannHilbert correspondence. 6.1. From divergences to iterated integrals. 6.2. From iterated integrals to differential systems. 6.3. Flat equisingular connections and vector bundles. 6.4. The "cosmic Galois group"7. The geometry of DimReg. 7.1. The motivic geometry of DimReg. 7.2. The noncommutative geometry of DimReg  8. Renormalization, singularities, and Hodge structures. 8.1. Projective radon transform. 8.2. The polar filtration and the Milnor fiber. 8.3. DimReg and mixed Hodge structures. 8.4. Regular and irregular singular connections  9. Beyond scalar theories. 9.1. Supermanifolds. 9.2. Parametric Feynman integrals and supermanifolds. 9.3. Graph supermanifolds. 9.4. Noncommutative field theories
An invitation to noncommutative geometry by
Masoud Khalkhali(
)
24 editions published in 2008 in English and held by 1,732 WorldCat member libraries worldwide
"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."BOOK JACKET
24 editions published in 2008 in English and held by 1,732 WorldCat member libraries worldwide
"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."BOOK JACKET
Arithmetic and geometry around quantization by
Özgür Ceyhan(
)
15 editions published in 2010 in English and held by 523 WorldCat member libraries worldwide
In recent decades, quantization has led to interesting applications in various mathematical branches. This volume, comprised of research and survey articles, discusses key topics, including symplectic and algebraic geometry, representation theory, quantum groups, the geometric Langlands program, quantum ergodicity, and noncommutative geometry. A wide range of topics related to quantization are covered, giving a glimpse of the broad subject. The articlesare written by distinguished mathematicians in the fieldand reflect subsequent developments followingthe Arithmetic and Geometry around Quantization conference held in Istanbul. List of Contributors: S. Akbulut R. Hadani S. Arkhipov K. Kremnizer Ö. Ceyhan S. Mahanta E. Frenkel S. Salur K. FukayaG. Ben Simon D. GaitsgoryW. van Suijlekom S. Gurevich
15 editions published in 2010 in English and held by 523 WorldCat member libraries worldwide
In recent decades, quantization has led to interesting applications in various mathematical branches. This volume, comprised of research and survey articles, discusses key topics, including symplectic and algebraic geometry, representation theory, quantum groups, the geometric Langlands program, quantum ergodicity, and noncommutative geometry. A wide range of topics related to quantization are covered, giving a glimpse of the broad subject. The articlesare written by distinguished mathematicians in the fieldand reflect subsequent developments followingthe Arithmetic and Geometry around Quantization conference held in Istanbul. List of Contributors: S. Akbulut R. Hadani S. Arkhipov K. Kremnizer Ö. Ceyhan S. Mahanta E. Frenkel S. Salur K. FukayaG. Ben Simon D. GaitsgoryW. van Suijlekom S. Gurevich
Noncommutative geometry and number theory : where arithmetic meets geometry and physics by
Caterina Consani(
)
15 editions published between 2006 and 2014 in English and held by 505 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
15 editions published between 2006 and 2014 in English and held by 505 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
Quantum groups and noncommutative spaces : perspectives on quantum geometry : a publication of the MaxPlanckInstitute for
Mathematics, Bonn by
Matilde Marcolli(
)
24 editions published between 2010 and 2014 in English and held by 496 WorldCat member libraries worldwide
This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differentialgeometric 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 MaxPlanckInstitute for Mathematics in Bonn. Contributions byTomasz Brzezinski, Branimir Cacic, Rita Fioresi, Rita Fioresi and Fabio Gavarini, Debashish Goswami, Christian Kassel, Avijit Mukherjee, Alfons Van Daele, Robert Wisbauer, Alessandro Zampini The volume is aimed as introducing techniques and results on Quantum Groups and Noncommutative Geometry, in a form that is accessible to other researchers in related areas as well as to advanced graduate students. The topics covered are of interest to both mathematicians and theoretical physicists. Prof. Dr. Matilde Marcolli, Department of Mathematics, California Institute of Technology, Pasadena, California, USA. Dr. Deepak Parashar, Cambridge Cancer Trials Centre and MRC Biostatistics Unit, University of Cambridge, United Kingdom
24 editions published between 2010 and 2014 in English and held by 496 WorldCat member libraries worldwide
This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differentialgeometric 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 MaxPlanckInstitute for Mathematics in Bonn. Contributions byTomasz Brzezinski, Branimir Cacic, Rita Fioresi, Rita Fioresi and Fabio Gavarini, Debashish Goswami, Christian Kassel, Avijit Mukherjee, Alfons Van Daele, Robert Wisbauer, Alessandro Zampini The volume is aimed as introducing techniques and results on Quantum Groups and Noncommutative Geometry, in a form that is accessible to other researchers in related areas as well as to advanced graduate students. The topics covered are of interest to both mathematicians and theoretical physicists. Prof. Dr. Matilde Marcolli, Department of Mathematics, California Institute of Technology, Pasadena, California, USA. Dr. Deepak Parashar, Cambridge Cancer Trials Centre and MRC Biostatistics Unit, University of Cambridge, United Kingdom
Deformation spaces : perspectives on algebrogeometric moduli by
Hossein Abbaspour(
)
20 editions published between 2002 and 2014 in English and Undetermined and held by 487 WorldCat member libraries worldwide
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 selfcontained and peerreviewed papers by experts which present uptodate 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 MaxPlanckInstitute for Mathematics and the Hausdorff Center for Mathematics in Bonn
20 editions published between 2002 and 2014 in English and Undetermined and held by 487 WorldCat member libraries worldwide
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 selfcontained and peerreviewed papers by experts which present uptodate 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 MaxPlanckInstitute for Mathematics and the Hausdorff Center for Mathematics in Bonn
Noncommutative geometry, quantum fields and motives by
Alain Connes(
Book
)
17 editions published between 2007 and 2019 in English and held by 372 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 motivic 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. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a RiemannHilbert correspondence. 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. 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 Qlattices used in the study of the zeta function
17 editions published between 2007 and 2019 in English and held by 372 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 motivic 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. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a RiemannHilbert correspondence. 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. 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 Qlattices used in the study of the zeta function
Arithmetic noncommutative geometry by
Matilde Marcolli(
Book
)
2 editions published in 2005 in English and held by 211 WorldCat member libraries worldwide
Arithmetic Noncommutative Geometry uses ideas and tools from noncommutative geometry to address questions in a new way and to reinterpret results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at Archimedean places of arithmetic surfaces and varieties. Noncommutative geometry can be expected to say something about topics of arithmetic interest because it provides the right framework for which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry. With a foreword written by Yuri Manin and a brief introduction to noncommutative geometry, this book offers a comprehensive account of the cross fertilization between two important areas, noncommutative geometry and number theory. It is suitable for graduate students and researchers interested in these areas
2 editions published in 2005 in English and held by 211 WorldCat member libraries worldwide
Arithmetic Noncommutative Geometry uses ideas and tools from noncommutative geometry to address questions in a new way and to reinterpret results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at Archimedean places of arithmetic surfaces and varieties. Noncommutative geometry can be expected to say something about topics of arithmetic interest because it provides the right framework for which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry. With a foreword written by Yuri Manin and a brief introduction to noncommutative geometry, this book offers a comprehensive account of the cross fertilization between two important areas, noncommutative geometry and number theory. It is suitable for graduate students and researchers interested in these areas
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
Bonn) Mini Workshop on Renormalization (2006(
Book
)
18 editions published between 2011 and 2012 in English and held by 202 WorldCat member libraries worldwide
18 editions published between 2011 and 2012 in English and held by 202 WorldCat member libraries worldwide
Frobenius manifolds : quantum cohomology and singularities : a publication of the MaxPlanckInstitute for Mathematics, Bonn by
Klaus Hertling(
Book
)
6 editions published in 2004 in English and held by 184 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
6 editions published in 2004 in English and held by 184 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
SeibergWitten gauge theory by
Matilde Marcolli(
Book
)
11 editions published between 1990 and 2011 in English and held by 143 WorldCat member libraries worldwide
11 editions published between 1990 and 2011 in English and held by 143 WorldCat member libraries worldwide
Noncommutative cosmology by
Matilde Marcolli(
Book
)
10 editions published between 2017 and 2018 in English and Undetermined and held by 76 WorldCat member libraries worldwide
10 editions published between 2017 and 2018 in English and Undetermined and held by 76 WorldCat member libraries worldwide
Arithmetic noncommutative geometry by
Matilde Marcolli(
Book
)
12 editions published in 2005 in English and held by 52 WorldCat member libraries worldwide
12 editions published in 2005 in English and held by 52 WorldCat member libraries worldwide
Noncommutative geometry, quantum fields and motives by
Alain Connes(
Book
)
1 edition published in 2008 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 2008 in English and held by 16 WorldCat member libraries worldwide
Some remarks on conjugacy classes of bundle gauge groups by
Matilde Marcolli(
Book
)
2 editions published in 1994 in English and held by 6 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 6 WorldCat member libraries worldwide
Weak UCP and perturbed monopole equations by
Bernhelm Booss(
Book
)
3 editions published in 2002 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 2002 in English and held by 5 WorldCat member libraries worldwide
Lectures on arithmetic noncommutative geometry by
Matilde Marcolli(
Book
)
2 editions published in 2004 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 2004 in English and held by 3 WorldCat member libraries worldwide
Lumen naturae : visions of space in art and mathematics by
Matilde Marcolli(
Book
)
2 editions published in 2017 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 2017 in English and held by 3 WorldCat member libraries worldwide
Notes on SeibergWitten gauge theory by
Matilde Marcolli(
Book
)
2 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide
Ave atque vale : poesie per un angelo by
Matilde Marcolli(
Book
)
2 editions published in 1987 in Italian and held by 3 WorldCat member libraries worldwide
2 editions published in 1987 in Italian and held by 3 WorldCat member libraries worldwide
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Related Identities
 Khalkhali, Masoud 1963 Author Editor
 World Scientific (Firm)
 MaxPlanckInstitut für Mathematik Other
 Manin, I︠U︡. I. Author of introduction Editor
 Ceyhan, Özgür Author Editor
 Consani, Caterina Author Editor
 Abbaspour, Hossein Author Editor
 Tradler, Thomas Other Editor
 Parashar, D. Other Editor
 Connes, Alain Author
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Associated Subjects
Algebra Algebraic stacks Cosmology Feynman integrals Frobenius algebras Frobenius manifolds Gauge fields (Physics) Geometric quantization Geometry Geometry, Algebraic Global analysis (Mathematics) 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