Spin Pin Structures And Real Enumerative Geometry

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Spin/pin-structures And Real Enumerative Geometry

Author : Xujia Chen
Publisher : World Scientific
ISBN 13 : 9811278555
Total Pages : 467 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Spin/pin-structures And Real Enumerative Geometry by : Xujia Chen

Download or read book Spin/pin-structures And Real Enumerative Geometry written by Xujia Chen and published by World Scientific. This book was released on 2023-12-04 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spin/Pin-structures on vector bundles have long featured prominently in differential geometry, in particular providing part of the foundation for the original proof of the renowned Atiyah-Singer Index Theory. More recently, they have underpinned the symplectic topology foundations of the so-called real sector of the mirror symmetry of string theory.This semi-expository three-part monograph provides an accessible introduction to Spin- and Pin-structures in general, demonstrates their role in the orientability considerations in symplectic topology, and presents their applications in enumerative geometry.Part I contains a systematic treatment of Spin/Pin-structures from different topological perspectives and may be suitable for an advanced undergraduate reading seminar. This leads to Part II, which systematically studies orientability problems for the determinants of real Cauchy-Riemann operators on vector bundles. Part III introduces enumerative geometry of curves in complex projective varieties and in symplectic manifolds, demonstrating some applications of the first two parts in the process. Two appendices review the Čech cohomology perspective on fiber bundles and Lie group covering spaces.

Quantum Field Theory, Supersymmetry, and Enumerative Geometry

Author : Daniel S. Freed
Publisher : American Mathematical Soc.
ISBN 13 : 0821834312
Total Pages : 297 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Quantum Field Theory, Supersymmetry, and Enumerative Geometry by : Daniel S. Freed

Download or read book Quantum Field Theory, Supersymmetry, and Enumerative Geometry written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2006 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents three weeks of lectures given at the Summer School on Quantum Field Theory, Supersymmetry, and Enumerative Geometry. With this volume, the Park City Mathematics Institute returns to the general topic of the first institute: the interplay between quantum field theory and mathematics.

Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects

Author : Frank Neumann
Publisher : Springer Nature
ISBN 13 : 3030789772
Total Pages : 223 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects by : Frank Neumann

Download or read book Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects written by Frank Neumann and published by Springer Nature. This book was released on 2021-09-29 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry. The contributions to this volume are based on original lectures by leading researchers at the LMS-CMI Research School on ‘Homotopy Theory and Arithmetic Geometry - Motivic and Diophantine Aspects’ and the Nelder Fellow Lecturer Series, which both took place at Imperial College London in the summer of 2018. The contribution by Brazelton, based on the lectures by Wickelgren, provides an introduction to arithmetic enumerative geometry, the notes of Cisinski present motivic sheaves and new cohomological methods for intersection theory, and Schlank’s contribution gives an overview of the use of étale homotopy theory for obstructions to the existence of rational points on algebraic varieties. Finally, the article by Asok and Østvær, based in part on the Nelder Fellow lecture series by Østvær, gives a survey of the interplay between motivic homotopy theory and affine algebraic geometry, with a focus on contractible algebraic varieties. Now a major trend in arithmetic geometry, this volume offers a detailed guide to the fascinating circle of recent applications of homotopy theory to number theory. It will be invaluable to research students entering the field, as well as postdoctoral and more established researchers.

Handbook of Homotopy Theory

Author : Haynes Miller
Publisher : CRC Press
ISBN 13 : 1351251619
Total Pages : 982 pages
Book Rating : 4.3/5 (512 download)

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Book Synopsis Handbook of Homotopy Theory by : Haynes Miller

Download or read book Handbook of Homotopy Theory written by Haynes Miller and published by CRC Press. This book was released on 2020-01-23 with total page 982 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.

Singularities Symposium--Łojasiewicz 70

Author : Bronisław Jakubczyk
Publisher :
ISBN 13 :
Total Pages : 300 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Singularities Symposium--Łojasiewicz 70 by : Bronisław Jakubczyk

Download or read book Singularities Symposium--Łojasiewicz 70 written by Bronisław Jakubczyk and published by . This book was released on 1998 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mirror Symmetry

Author : Kentaro Hori
Publisher : American Mathematical Soc.
ISBN 13 : 0821829556
Total Pages : 954 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mirror Symmetry by : Kentaro Hori

Download or read book Mirror Symmetry written by Kentaro Hori and published by American Mathematical Soc.. This book was released on 2003 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.

Lectures on Field Theory and Topology

Author : Daniel S. Freed
Publisher : American Mathematical Soc.
ISBN 13 : 1470452065
Total Pages : 186 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Lectures on Field Theory and Topology by : Daniel S. Freed

Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.

Mathematics and Computation

Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

The Shape of Inner Space

Author : Shing-Tung Yau
Publisher : Il Saggiatore
ISBN 13 : 0465020232
Total Pages : 398 pages
Book Rating : 4.4/5 (65 download)

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Book Synopsis The Shape of Inner Space by : Shing-Tung Yau

Download or read book The Shape of Inner Space written by Shing-Tung Yau and published by Il Saggiatore. This book was released on 2010-09-07 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 984 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2001 with total page 984 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Modular Forms and String Duality

Author : Noriko Yui
Publisher : American Mathematical Soc.
ISBN 13 : 0821844849
Total Pages : 320 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Modular Forms and String Duality by : Noriko Yui

Download or read book Modular Forms and String Duality written by Noriko Yui and published by American Mathematical Soc.. This book was released on 2008 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is a testimony to the BIRS Workshop, and it covers a wide range of topics at the interface of number theory and string theory, with special emphasis on modular forms and string duality. They include the recent advances as well as introductory expositions on various aspects of modular forms, motives, differential equations, conformal field theory, topological strings and Gromov-Witten invariants, mirror symmetry, and homological mirror symmetry. The contributions are roughly divided into three categories: arithmetic and modular forms, geometric and differential equations, and physics and string theory. The book is suitable for researchers working at the interface of number theory and string theory."--BOOK JACKET.

Sharpening Mathematical Analysis Skills

Author : Alina Sîntămărian
Publisher : Springer Nature
ISBN 13 : 3030771393
Total Pages : 543 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Sharpening Mathematical Analysis Skills by : Alina Sîntămărian

Download or read book Sharpening Mathematical Analysis Skills written by Alina Sîntămărian and published by Springer Nature. This book was released on 2021-10-25 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers together a novel collection of problems in mathematical analysis that are challenging and worth studying. They cover most of the classical topics of a course in mathematical analysis, and include challenges presented with an increasing level of difficulty. Problems are designed to encourage creativity, and some of them were especially crafted to lead to open problems which might be of interest for students seeking motivation to get a start in research. The sets of problems are comprised in Part I. The exercises are arranged on topics, many of them being preceded by supporting theory. Content starts with limits, series of real numbers and power series, extending to derivatives and their applications, partial derivatives and implicit functions. Difficult problems have been structured in parts, helping the reader to find a solution. Challenges and open problems are scattered throughout the text, being an invitation to discover new original methods for proving known results and establishing new ones. The final two chapters offer ambitious readers splendid problems and two new proofs of a famous quadratic series involving harmonic numbers. In Part II, the reader will find solutions to the proposed exercises. Undergraduate students in mathematics, physics and engineering, seeking to strengthen their skills in analysis, will most benefit from this work, along with instructors involved in math contests, individuals who want to enrich and test their knowledge in analysis, and anyone willing to explore the standard topics of mathematical analysis in ways that aren’t commonly seen in regular textbooks.

The Geometry of Four-manifolds

Author : S. K. Donaldson
Publisher : Oxford University Press
ISBN 13 : 9780198502692
Total Pages : 464 pages
Book Rating : 4.5/5 (26 download)

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Book Synopsis The Geometry of Four-manifolds by : S. K. Donaldson

Download or read book The Geometry of Four-manifolds written by S. K. Donaldson and published by Oxford University Press. This book was released on 1997 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides an accessible account to the modern study of the geometry of four-manifolds. Prerequisites are a firm grounding in differential topology and geometry, as may be gained from the first year of a graduate course.

Understanding Philosophy of Science

Author : James Ladyman
Publisher : Routledge
ISBN 13 : 1134597908
Total Pages : 312 pages
Book Rating : 4.1/5 (345 download)

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Book Synopsis Understanding Philosophy of Science by : James Ladyman

Download or read book Understanding Philosophy of Science written by James Ladyman and published by Routledge. This book was released on 2012-08-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Few can imagine a world without telephones or televisions; many depend on computers and the Internet as part of daily life. Without scientific theory, these developments would not have been possible. In this exceptionally clear and engaging introduction to philosophy of science, James Ladyman explores the philosophical questions that arise when we reflect on the nature of the scientific method and the knowledge it produces. He discusses whether fundamental philosophical questions about knowledge and reality might be answered by science, and considers in detail the debate between realists and antirealists about the extent of scientific knowledge. Along the way, central topics in philosophy of science, such as the demarcation of science from non-science, induction, confirmation and falsification, the relationship between theory and observation and relativism are all addressed. Important and complex current debates over underdetermination, inference to the best explaination and the implications of radical theory change are clarified and clearly explained for those new to the subject.

Compact Manifolds with Special Holonomy

Author : Dominic D. Joyce
Publisher : OUP Oxford
ISBN 13 : 9780198506010
Total Pages : 460 pages
Book Rating : 4.5/5 (6 download)

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Book Synopsis Compact Manifolds with Special Holonomy by : Dominic D. Joyce

Download or read book Compact Manifolds with Special Holonomy written by Dominic D. Joyce and published by OUP Oxford. This book was released on 2000 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a combination of a graduate textbook on Reimannian holonomy groups, and a research monograph on compact manifolds with the exceptional holonomy groups G2 and Spin (7). It contains much new research and many new examples.

The Material Theory of Induction

Author : John D. Norton
Publisher : Bsps Open
ISBN 13 : 9781773852539
Total Pages : 0 pages
Book Rating : 4.8/5 (525 download)

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Book Synopsis The Material Theory of Induction by : John D. Norton

Download or read book The Material Theory of Induction written by John D. Norton and published by Bsps Open. This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The inaugural title in the new, Open Access series BSPS Open, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it. Which that is, and its extent, is determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference."--

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Author : Sirakov Boyan
Publisher : World Scientific
ISBN 13 : 9813272899
Total Pages : 5396 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Sirakov Boyan

Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Sirakov Boyan and published by World Scientific. This book was released on 2019-02-27 with total page 5396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.