WorldCat Identities

Marcolli, Matilde

Overview
Works: 92 works in 279 publications in 2 languages and 6,673 library holdings
Genres: Conference papers and proceedings 
Roles: Author, Editor, Other, Thesis advisor
Publication Timeline
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Most widely held works by Matilde Marcolli
Feynman motives by Matilde Marcolli( )

20 editions published between 2009 and 2010 in English and held by 1,719 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. One-particle-irreducible 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. Non-isolated 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. Deletion-contraction 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 Gelfand-Leray forms. 4.1. Oscillatory integrals. 4.2. Leray regularization of Feynman integrals -- 5. Connes-Kreimer theory in a nutshell. 5.1. The Bogolyubov recursion. 5.2. Hopf algebras and affine group schemes. 5.3. The Connes-Kreimer Hopf algebra. 5.4. Birkhoff factorization. 5.5. Factorization and Rota-Baxter algebras. 5.6. Motivic Feynman rules and Rota-Baxter structure -- 6. The Riemann-Hilbert 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( )

23 editions published in 2008 in English and held by 1,675 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 503 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 non-commutative 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 501 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 K-Theory. This volume collects and presents up-to-date 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 p-adic 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 Max-Planck-Institute for Mathematics, Bonn by Matilde Marcolli( )

21 editions published between 2010 and 2014 in English and held by 474 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 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. 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 algebro-geometric moduli by Hossein Abbaspour( )

19 editions published between 2002 and 2014 in English and Undetermined and held by 473 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 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. Contributions by Grégory Ginot, Thomas M. Fiore and Igor Kriz, Toshiro Hiranouchi and Satoshi Mochizuki, Paulo Carrillo Rouse, Donatella Iacono and Marco Manetti, John Terilla, Anne Pichereau - Researchers in the fields of deformation theory, noncommutative geometry, algebraic topology, mathematical physics - Advanced graduate students in mathematics Dr. Hossein Abbaspour, Department of Mathematics, Université de Nantes, France. Prof. Dr. Matilde Marcolli, Department of Mathematics, California Institute of Technology, Pasadena, California, USA. Dr. Thomas Tradler, Department of Mathematics, New York City College of Technology (CUNY), New York, USA
Noncommutative geometry, quantum fields and motives by Alain Connes( Book )

15 editions published between 2007 and 2012 in English and held by 363 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: 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 dea
Arithmetic noncommutative geometry by Matilde Marcolli( Book )

2 editions published in 2005 in English and held by 207 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 : 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 Bonn) Mini Workshop on Renormalization (2006( Book )

16 editions published between 2011 and 2012 in English and held by 199 WorldCat member libraries worldwide

Frobenius manifolds : quantum cohomology and singularities : a publication of the Max-Planck-Institute for Mathematics, Bonn by Claus Hertling( Book )

7 editions published in 2004 in English and held by 178 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
Seiberg-Witten gauge theory by Matilde Marcolli( Book )

9 editions published between 1999 and 2011 in English and held by 141 WorldCat member libraries worldwide

Noncommutative cosmology by Matilde Marcolli( Book )

10 editions published between 2017 and 2018 in English and Undetermined and held by 68 WorldCat member libraries worldwide

Arithmetic noncommutative geometry by Matilde Marcolli( Book )

9 editions published in 2005 in English and held by 47 WorldCat member libraries worldwide

Noncommutative geometry, quantum fields and motives by Alain Connes( Book )

1 edition published in 2008 in English and held by 15 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

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

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

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

Notes on Seiberg-Witten gauge theory by Matilde Marcolli( Book )

2 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide

 
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WorldCat IdentitiesRelated Identities
Noncommutative geometry and number theory : where arithmetic meets geometry and physics
Covers
An invitation to noncommutative geometryArithmetic and geometry around quantizationNoncommutative geometry and number theory : where arithmetic meets geometry and physicsQuantum groups and noncommutative spaces : perspectives on quantum geometry : a publication of the Max-Planck-Institute for Mathematics, BonnDeformation spaces : perspectives on algebro-geometric moduliNoncommutative geometry, quantum fields and motivesArithmetic noncommutative geometryCombinatorics 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
Alternative Names
Matilde Marcolli Italiaans wiskundige

Matilde Marcolli Italian mathematician and physicist

Matilde Marcolli italienische Mathematikerin

Languages
English (190)

Italian (2)