The Aksz Construction In Derived Algebraic Geometry As An Extended Topological Field Theory
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The Aksz Construction In Derived Algebraic Geometry As An Extended Topological Field Theory
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Author : Damien Calaque
language : en
Publisher: American Mathematical Society
Release Date : 2025-05-29
The Aksz Construction In Derived Algebraic Geometry As An Extended Topological Field Theory written by Damien Calaque and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-29 with Mathematics categories.
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Moduli Spaces Virtual Invariants And Shifted Symplectic Structures
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Author : Young-Hoon Kiem
language : en
Publisher: Springer Nature
Release Date : 2025-03-25
Moduli Spaces Virtual Invariants And Shifted Symplectic Structures written by Young-Hoon Kiem and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-25 with Mathematics categories.
Enumerative geometry is a core area of algebraic geometry that dates back to Apollonius in the second century BCE. It asks for the number of geometric figures with desired properties and has many applications from classical geometry to modern physics. Typically, an enumerative geometry problem is solved by first constructing the space of all geometric figures of fixed type, called the moduli space, and then finding the subspace of objects satisfying the desired properties. Unfortunately, many moduli spaces from nature are highly singular, and an intersection theory is difficult to make sense of. However, they come with deeper structures, such as perfect obstruction theories, which enable us to define nice subsets, called virtual fundamental classes. Now, enumerative numbers, called virtual invariants, are defined as integrals against the virtual fundamental classes. Derived algebraic geometry is a relatively new area of algebraic geometry that is a natural generalization of Serre’s intersection theory in the 1950s and Grothendieck’s scheme theory in the 1960s. Many moduli spaces in enumerative geometry admit natural derived structures as well as shifted symplectic structures. The book covers foundations on derived algebraic and symplectic geometry. Then, it covers foundations on virtual fundamental classes and moduli spaces from a classical algebraic geometry point of view. Finally, it fuses derived algebraic geometry with enumerative geometry and covers the cutting-edge research topics about Donaldson–Thomas invariants in dimensions three and four.
New Spaces In Physics
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Author : Mathieu Anel
language : en
Publisher: Cambridge University Press
Release Date : 2021-04
New Spaces In Physics written by Mathieu Anel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04 with Mathematics categories.
In this graduate-level book, leading researchers explore various new notions of 'space' in mathematical physics.
String Math 2013
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Author : Ron Donagi, Michael R. Douglas
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-02
String Math 2013 written by Ron Donagi, Michael R. Douglas and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-02 with Mathematics categories.
This volume contains the proceedings of the conference `String-Math 2013' which was held June 17-21, 2013 at the Simons Center for Geometry and Physics at Stony Brook University. This was the third in a series of annual meetings devoted to the interface of mathematics and string theory. Topics include the latest developments in supersymmetric and topological field theory, localization techniques, the mathematics of quantum field theory, superstring compactification and duality, scattering amplitudes and their relation to Hodge theory, mirror symmetry and two-dimensional conformal field theory, and many more. This book will be important reading for researchers and students in the area, and for all mathematicians and string theorists who want to update themselves on developments in the math-string interface.
Mathematical Aspects Of Quantum Field Theories
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Author : Damien Calaque
language : en
Publisher: Springer
Release Date : 2015-01-06
Mathematical Aspects Of Quantum Field Theories written by Damien Calaque and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-06 with Science categories.
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.
Algebraic Geometry Salt Lake City 2015
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Author : Richard Thomas
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-06-01
Algebraic Geometry Salt Lake City 2015 written by Richard Thomas and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-01 with Mathematics categories.
This is Part 2 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.
Noncommutative Geometry And Physics 4 Workshop On Strings Membranes And Topological Field Theory
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Author : Yoshiaki Maeda
language : en
Publisher: World Scientific
Release Date : 2017-03-16
Noncommutative Geometry And Physics 4 Workshop On Strings Membranes And Topological Field Theory written by Yoshiaki Maeda and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-16 with Mathematics categories.
This book is a collection of the lectures and talks presented in the Tohoku Forum for Creativity in the thematic year 2015 'Fundamental Problems in Quantum Physics: Strings, Black Holes and Quantum Information', and related events in the period 2014-2016.This volume especially contains an overview of recent developments in the theory of strings and membranes, as well as topological field theory.
A Study In Derived Algebraic Geometry
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Author : Dennis Gaitsgory
language : en
Publisher: American Mathematical Soc.
Release Date : 2017
A Study In Derived Algebraic Geometry written by Dennis Gaitsgory and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in various parts of mathematics, most prominently in representation theory. This volume develops the theory of ind-coherent sheaves in the context of derived algebraic geometry. Ind-coherent sheaves are a “renormalization” of quasi-coherent sheaves and provide a natural setting for Grothendieck-Serre duality as well as geometric incarnations of numerous categories of interest in representation theory. This volume consists of three parts and an appendix. The first part is a survey of homotopical algebra in the setting of -categories and the basics of derived algebraic geometry. The second part builds the theory of ind-coherent sheaves as a functor out of the category of correspondences and studies the relationship between ind-coherent and quasi-coherent sheaves. The third part sets up the general machinery of the -category of correspondences needed for the second part. The category of correspondences, via the theory developed in the third part, provides a general framework for Grothendieck's six-functor formalism. The appendix provides the necessary background on -categories needed for the third part.
Constructing The Topological Field Theory Associated To A Cyclic A Infinity Algebra
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Author : Weng-Him Cheung
language : en
Publisher:
Release Date : 2022
Constructing The Topological Field Theory Associated To A Cyclic A Infinity Algebra written by Weng-Him Cheung and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
In 1988, Atiyah proposed a set of axioms for topological field theories. Later, the notion ofan extended topological field theory, expressed in the language of higher category theory, emerged. One such type of topological field theory was studied by Costello. Costello proved that a partial analog of the correspondence between 2-dimensional topological field theories (under Atiyah's formalism) and Frobenius algebras holds for his topological field theories. In particular, given a cyclic A[infinity]-algebra, one can construct a positive-boundary 2-dimensional topological field theory associated to it. His construction, however, did not provide explicitly computable formulas for the maps. Kontsevich and Soibelman later sketched these formulas, but they did not discuss the signs involved. We describe how to compute these signs and show that with our signs, Kontsevich and Soibelman's formulas do in fact give the information of a topological field theory.
Operads In Algebra Topology And Physics
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Author : Martin Markl
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Operads In Algebra Topology And Physics written by Martin Markl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Operads are mathematical devices which describe algebraic structures of many varieties and in various categories. From their beginnings in the 1960s, they have developed to encompass such areas as combinatorics, knot theory, moduli spaces, string field theory and deformation quantization.