Fourier Mukai And Nahm Transforms In Geometry And Mathematical Physics
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Fourier Mukai And Nahm Transforms In Geometry And Mathematical Physics
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Author : CLAUDIO BARTOCCI
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-12
Fourier Mukai And Nahm Transforms In Geometry And Mathematical Physics written by CLAUDIO BARTOCCI and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-12 with Science categories.
Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries. In the last three decades the development of a number of novel ideas in algebraic geometry, category theory, gauge theory, and string theory has been closely related to generalizations of integral transforms of a more geometric character. "Fourier–Mukai and Nahm Transforms in Geometry and Mathematical Physics" examines the algebro-geometric approach (Fourier–Mukai functors) as well as the differential-geometric constructions (Nahm). Also included is a considerable amount of material from existing literature which has not been systematically organized into a monograph. Key features: Basic constructions and definitions are presented in preliminary background chapters - Presentation explores applications and suggests several open questions - Extensive bibliography and index. This self-contained monograph provides an introduction to current research in geometry and mathematical physics and is intended for graduate students and researchers just entering this field.
Fourier Mukai And Nahm Transforms In Geometry And Mathematical Physics
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Author : CLAUDIO BARTOCCI
language : en
Publisher: Birkhäuser
Release Date : 2011-09-27
Fourier Mukai And Nahm Transforms In Geometry And Mathematical Physics written by CLAUDIO BARTOCCI and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-27 with Science categories.
Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries. In the last three decades the development of a number of novel ideas in algebraic geometry, category theory, gauge theory, and string theory has been closely related to generalizations of integral transforms of a more geometric character. "Fourier–Mukai and Nahm Transforms in Geometry and Mathematical Physics" examines the algebro-geometric approach (Fourier–Mukai functors) as well as the differential-geometric constructions (Nahm). Also included is a considerable amount of material from existing literature which has not been systematically organized into a monograph. Key features: Basic constructions and definitions are presented in preliminary background chapters - Presentation explores applications and suggests several open questions - Extensive bibliography and index. This self-contained monograph provides an introduction to current research in geometry and mathematical physics and is intended for graduate students and researchers just entering this field.
Nahm And Fourier Mukai Transforms In Geometry And Mathematical Physics
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Author :
language : en
Publisher:
Release Date : 2009
Nahm And Fourier Mukai Transforms In Geometry And Mathematical Physics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
New Trends In Geometry
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Author : Claudio Bartocci
language : en
Publisher: World Scientific
Release Date : 2011
New Trends In Geometry written by Claudio Bartocci and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This volume focuses on the interactions between mathematics, physics, biology and neuroscience by exploring new geometrical and topological modeling in these fields. Among the highlights are the central roles played by multilevel and scale-change approaches in these disciplines. The integration of mathematics with physics, molecular and cell biology, and the neurosciences, will constitute the new frontier and challenge for 21st century science, where breakthroughs are more likely to span across traditional disciplines.
Moduli Spaces And Vector Bundles
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Author : Leticia Brambila-Paz
language : en
Publisher: Cambridge University Press
Release Date : 2009-05-21
Moduli Spaces And Vector Bundles written by Leticia Brambila-Paz 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 2009-05-21 with Mathematics categories.
Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry. In recent decades this subject has been greatly enhanced by its relationships with other areas of mathematics, including differential geometry, topology and even theoretical physics, specifically gauge theory, quantum field theory and string theory. Peter E. Newstead has been a leading figure in this field almost from its inception and has made many seminal contributions to our understanding of moduli spaces of stable bundles. This volume has been assembled in tribute to Professor Newstead and his contribution to algebraic geometry. Some of the subject's leading experts cover foundational material, while the survey and research papers focus on topics at the forefront of the field. This volume is suitable for both graduate students and more experienced researchers.
Introduction To String Theory
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Author : Sergio Cecotti
language : en
Publisher: Springer Nature
Release Date : 2023-10-06
Introduction To String Theory written by Sergio Cecotti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-06 with Science categories.
Graduate students typically enter into courses on string theory having little to no familiarity with the mathematical background so crucial to the discipline. As such, this book, based on lecture notes, edited and expanded, from the graduate course taught by the author at SISSA and BIMSA, places particular emphasis on said mathematical background. The target audience for the book includes students of both theoretical physics and mathematics. This explains the book’s "strange" style: on the one hand, it is highly didactic and explicit, with a host of examples for the physicists, but, in addition, there are also almost 100 separate technical boxes, appendices, and starred sections, in which matters discussed in the main text are put into a broader mathematical perspective, while deeper and more rigorous points of view (particularly those from the modern era) are presented. The boxes also serve to further shore up the reader’s understanding of the underlying math. In writing this book, the author’s goal was not to achieve any sort of definitive conciseness, opting instead for clarity and "completeness". To this end, several arguments are presented more than once from different viewpoints and in varying contexts.
Coherent States And Their Applications
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Author : Jean-Pierre Antoine
language : en
Publisher: Springer
Release Date : 2018-06-01
Coherent States And Their Applications written by Jean-Pierre Antoine and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-01 with Science categories.
Coherent states (CS) were originally introduced in 1926 by Schrödinger and rediscovered in the early 1960s in the context of laser physics. Since then, they have evolved into an extremely rich domain that pervades virtually every corner of physics, and have also given rise to a range of research topics in mathematics. The purpose of the 2016 CIRM conference was to bring together leading experts in the field with scientists interested in related topics, to jointly investigate their applications in physics, their various mathematical properties, and their generalizations in many directions. Instead of traditional proceedings, this book presents sixteen longer review-type contributions, which are the outcome of a collaborative effort by many conference participants, subsequently reviewed by independent experts. The book aptly illustrates the diversity of CS aspects, from purely mathematical topics to physical applications, including quantum gravity.
Helix Structures In Quantum Cohomology Of Fano Varieties
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Author : Giordano Cotti
language : en
Publisher: Springer Nature
Release Date : 2024-10-28
Helix Structures In Quantum Cohomology Of Fano Varieties written by Giordano Cotti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-28 with Mathematics categories.
This research monograph provides a comprehensive study of a conjecture initially proposed by the second author at the 1998 International Congress of Mathematicians (ICM). This conjecture asserts the equivalence, for a Fano variety, between the semisimplicity condition of its quantum cohomology and the existence of full exceptional collections in its derived category of coherent sheaves. Additionally, in its quantitative form, the conjecture specifies an explicit relation between the monodromy data of the quantum cohomology, characteristic classes, and exceptional collections. A refined version of the conjecture is introduced, with a particular focus on the central connection matrix, and a precise link is established between this refined conjecture and Γ-conjecture II, as proposed by S. Galkin, V. Golyshev, and H. Iritani. By performing explicit calculations of the monodromy data, the validity of the refined conjecture for all complex Grassmannians G(r,k) is demonstrated. Intended for students and researchers, the book serves as an introduction to quantum cohomology and its isomonodromic approach, along with its algebraic counterpart in the derived category of coherent sheaves.
Vector Bundles And Complex Geometry
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Author : Oscar García-Prada
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Vector Bundles And Complex Geometry written by Oscar García-Prada 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 2010 with Mathematics categories.
This volume contains a collection of papers from the Conference on Vector Bundles held at Miraflores de la Sierra, Madrid, Spain on June 16-20, 2008, which honored S. Ramanan on his 70th birthday. The main areas covered in this volume are vector bundles, parabolic bundles, abelian varieties, Hilbert schemes, contact structures, index theory, Hodge theory, and geometric invariant theory. Professor Ramanan has made important contributions in all of these areas.
The Mathematical And Philosophical Legacy Of Alexander Grothendieck
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Author : Marco Panza
language : en
Publisher: Springer Nature
Release Date : 2025-01-21
The Mathematical And Philosophical Legacy Of Alexander Grothendieck written by Marco Panza and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-21 with Mathematics categories.
Alexander Grothendieck is often considered one of the greatest mathematicians of the twentieth century (if not all time), and his unique vision continues to impact and inspire many fields and researchers today. Utilizing a multidisciplinary approach, this edited volume explores the profound influence his work and ideas have had not only on mathematics, but also on logic and philosophy. Chapters are written by international scholars, and many were inspired by talks given at the conference “Grothendieck, A Multifarious Giant” at Chapman University (May 24-28, 2022). Some chapters are written from a historical perspective and discuss the development of the main themes that characterized Grothendieck's work. Others are more mathematical in nature, analyzing and extending some of his more relevant and obscure results that are still not well understood. Philosophical implications and applications in logic are the subjects of other chapters. This volume will be of interest not only to mathematicians working in algebraic geometry, category theory, and other areas to which Grothendieck contributed, but also to philosophers, logicians, and historians of science.