Marcolli, Matilde
Overview
Works:  95 works in 250 publications in 2 languages and 6,065 library holdings 

Genres:  Conference papers and proceedings Academic theses 
Roles:  Author, Editor, Thesis advisor 
Classifications:  QA641, 512.55 
Publication Timeline
.
Most widely held works by
Matilde Marcolli
Noncommutative geometry, quantum fields and motives by
Alain Connes(
Book
)
12 editions published between 2005 and 2008 in English and held by 338 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."Jacket
12 editions published between 2005 and 2008 in English and held by 338 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."Jacket
Arithmetic noncommutative geometry by
Matilde Marcolli(
Book
)
12 editions published between 2004 and 2005 in English and held by 223 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
12 editions published between 2004 and 2005 in English and held by 223 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
Feynman motives by
Matilde Marcolli(
Book
)
19 editions published between 2009 and 2010 in English and held by 198 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
19 editions published between 2009 and 2010 in English and held by 198 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
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
)
14 editions published in 2011 in English and held by 151 WorldCat member libraries worldwide
14 editions published in 2011 in English and held by 151 WorldCat member libraries worldwide
SeibergWitten gauge theory by
Matilde Marcolli(
Book
)
14 editions published between 1990 and 2011 in English and held by 139 WorldCat member libraries worldwide
14 editions published between 1990 and 2011 in English and held by 139 WorldCat member libraries worldwide
Noncommutative geometry and number theory : where arithmetic meets geometry and physics by
Caterina Consani(
Book
)
14 editions published between 2006 and 2014 in English and held by 129 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
14 editions published between 2006 and 2014 in English and held by 129 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
An invitation to noncommutative geometry by
Masoud Khalkhali(
Book
)
18 editions published in 2008 in English and Undetermined and held by 114 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
18 editions published in 2008 in English and Undetermined and held by 114 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
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 111 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 111 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
Arithmetic and geometry around quantization by
Özgür Ceyhan(
Book
)
15 editions published in 2010 in English and held by 110 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 110 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
Deformation spaces : perspectives on algebrogeometric moduli by
Hossein Abbaspour(
Book
)
16 editions published between 2002 and 2014 in English and held by 99 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. 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
16 editions published between 2002 and 2014 in English and held by 99 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. 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
Quantum groups and noncommutative spaces : perspectives on quantum geometry : a publication of the MaxPlanckInstitute for
Mathematics, Bonn by
Matilde Marcolli(
Book
)
14 editions published between 2011 and 2014 in English and held by 82 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
14 editions published between 2011 and 2014 in English and held by 82 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
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] by
Matilde Marcolli(
)
3 editions published in 2011 in English and held by 12 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
3 editions published in 2011 in English and held by 12 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
Some remarks on conjugacy classes of bundle gauge groups by
Matilde Marcolli(
Book
)
3 editions published in 1994 in English and held by 7 WorldCat member libraries worldwide
3 editions published in 1994 in English and held by 7 WorldCat member libraries worldwide
Equivariant SeibergWitten Floer homology by
Matilde Marcolli(
Book
)
4 editions published between 1996 and 2002 in English and held by 4 WorldCat member libraries worldwide
4 editions published between 1996 and 2002 in English and held by 4 WorldCat member libraries worldwide
Weak UCP and perturbed monopole equations by
Bernhelm Booss(
Book
)
2 editions published in 2002 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 2002 in English and held by 3 WorldCat member libraries worldwide
Ave atque vale : poesie per un angelo by
Matilde Marcolli(
Book
)
1 edition published in 1987 in Italian and held by 2 WorldCat member libraries worldwide
1 edition published in 1987 in Italian and held by 2 WorldCat member libraries worldwide
Lumen naturae : visions of space in art and mathematics by
Matilde Marcolli(
Book
)
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
Geography and botany of irreducible symplectic 4manifolds with abelian fundamental group by Rafael Torres Ruiz(
)
2 editions published in 2010 in English and held by 2 WorldCat member libraries worldwide
In this thesis the geography and botany of irreducible symplectic 4manifolds with abelian fundamental group of small rank are studied. It resembles an anthology of the contribution obtained by the author during his infatuation with 4dimensional topology by studying its recent developments. As such, each chapter is independent from each other and the reader is welcomed to start reading whichever one seems more appealing. We now give an outline for the sake of convenience. The first chapter of the thesis deals with the existence and (lack of) uniqueness of smooth irreducible symplectic nonspin 4manifolds with cyclic fundamental group (both finite and infinite). Chapter 2 does the same for 4manifolds with abelian, yet noncyclic $\pi_1$; the use of the homeomorphism criteria on these manifolds due to I. Hambleton and M. Kreck is of interest. In Chapter 3, the Spin geography for abelian fundamental groups of small rank is studied. A couple of subtle relations between simply connected and nonsimply connected exotic 4manifolds are explored through out the fourth chapter. Chapter 5 gives closure to a question raised in Chapter 4, and describes current research projects pursued by the author. These projects came naturally through the results presented in previous chapters. The thesis ends by describing two research progress that are being pursued. Chapter 6 contains the current situation regarding the geography and botany of spin manifolds with zero signature. The current state of the joint work of the author with Jonathan Yazinski (at McMaster University at the time of writing) is described in the seventh and final chapter
2 editions published in 2010 in English and held by 2 WorldCat member libraries worldwide
In this thesis the geography and botany of irreducible symplectic 4manifolds with abelian fundamental group of small rank are studied. It resembles an anthology of the contribution obtained by the author during his infatuation with 4dimensional topology by studying its recent developments. As such, each chapter is independent from each other and the reader is welcomed to start reading whichever one seems more appealing. We now give an outline for the sake of convenience. The first chapter of the thesis deals with the existence and (lack of) uniqueness of smooth irreducible symplectic nonspin 4manifolds with cyclic fundamental group (both finite and infinite). Chapter 2 does the same for 4manifolds with abelian, yet noncyclic $\pi_1$; the use of the homeomorphism criteria on these manifolds due to I. Hambleton and M. Kreck is of interest. In Chapter 3, the Spin geography for abelian fundamental groups of small rank is studied. A couple of subtle relations between simply connected and nonsimply connected exotic 4manifolds are explored through out the fourth chapter. Chapter 5 gives closure to a question raised in Chapter 4, and describes current research projects pursued by the author. These projects came naturally through the results presented in previous chapters. The thesis ends by describing two research progress that are being pursued. Chapter 6 contains the current situation regarding the geography and botany of spin manifolds with zero signature. The current state of the joint work of the author with Jonathan Yazinski (at McMaster University at the time of writing) is described in the seventh and final chapter
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Related Identities
 Khalkhali, Masoud 1963
 MaxPlanckInstitut für Mathematik
 World Scientific (Firm)
 Manin, I︠U︡. I. Author of introduction Author Editor
 Consani, Caterina Author Editor
 Ceyhan, Özgür Author Editor
 Abbaspour, Hossein Author Editor
 Tradler, Thomas Editor
 Parashar, D. Editor
 Connes, Alain Author
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Associated Subjects
Abelian groups Algebra Algebraic stacks Feynman integrals Fourmanifolds (Topology) 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