Advances in Algebraic Geometry Motivated by Physics

Advances in Algebraic Geometry Motivated by Physics PDF Author: Emma Previato
Publisher: American Mathematical Soc.
ISBN: 082182810X
Category : Mathematics
Languages : en
Pages : 310

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Book Description
Our knowledge of objects of algebraic geometry such as moduli of curves, (real) Schubert classes, fundamental groups of complements of hyperplane arrangements, toric varieties, and variation of Hodge structures, has been enhanced recently by ideas and constructions of quantum field theory, such as mirror symmetry, Gromov-Witten invariants, quantum cohomology, and gravitational descendants. These are some of the themes of this refereed collection of papers, which grew out of the special session, ``Enumerative Geometry in Physics,'' held at the AMS meeting in Lowell, MA, April 2000. This session brought together mathematicians and physicists who reported on the latest results and open questions; all the abstracts are included as an Appendix, and also included are papers by some who could not attend. The collection provides an overview of state-of-the-art tools, links that connect classical and modern problems, and the latest knowledge available.

Algebraic Geometry

Algebraic Geometry PDF Author: Joe Harris
Publisher: Springer Science & Business Media
ISBN: 1475721897
Category : Mathematics
Languages : en
Pages : 344

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Book Description
"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship." --MATHEMATICAL REVIEWS

Differential Geometry For Physicists

Differential Geometry For Physicists PDF Author: Bo-yu Hou
Publisher: World Scientific Publishing Company
ISBN: 9813105097
Category : Science
Languages : en
Pages : 561

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Book Description
This book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8-10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics.

Algebraic Methods in Statistics and Probability

Algebraic Methods in Statistics and Probability PDF Author: Marlos A. G. Viana
Publisher: American Mathematical Soc.
ISBN: 0821826875
Category : Mathematics
Languages : en
Pages : 354

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Book Description
The 23 papers report recent developments in using the technique to help clarify the relationship between phenomena and data in a number of natural and social sciences. Among the topics are a coordinate-free approach to multivariate exponential families, some rank-based hypothesis tests for covariance structure and conditional independence, deconvolution density estimation on compact Lie groups, random walks on regular languages and algebraic systems of generating functions, and the extendibility of statistical models. There is no index. c. Book News Inc.

The Geometry of Physics

The Geometry of Physics PDF Author: Theodore Frankel
Publisher: Cambridge University Press
ISBN: 1139505610
Category : Mathematics
Languages : en
Pages : 749

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Book Description
This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang–Mills, the Aharonov–Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.

Physics for Mathematicians

Physics for Mathematicians PDF Author: Michael Spivak
Publisher:
ISBN: 9780914098324
Category : Mechanics
Languages : en
Pages : 733

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Book Description


Algebraic Statistics for Computational Biology

Algebraic Statistics for Computational Biology PDF Author: L. Pachter
Publisher: Cambridge University Press
ISBN: 9780521857000
Category : Mathematics
Languages : en
Pages : 440

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Book Description
This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.

A Mathematical Mosaic

A Mathematical Mosaic PDF Author: Ravi Vakil
Publisher: Brendan Kelly Publishing Inc.
ISBN: 9781895997040
Category : Juvenile Nonfiction
Languages : sa
Pages : 258

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Book Description
Powerful problem solving ideas that focus on the major branches of mathematics and their interconnections.

Structured Matrices in Mathematics, Computer Science, and Engineering I

Structured Matrices in Mathematics, Computer Science, and Engineering I PDF Author: Vadim Olshevsky
Publisher: American Mathematical Soc.
ISBN: 0821819216
Category : Matrices
Languages : en
Pages : 346

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Book Description
"The collection of the contributions to these volumes offers a flavor of the plethora of different approaches to attack structured matrix problems. The reader will find that the theory of structured matrices is positioned to bridge diverse applications in the sciences and engineering, deep mathematical theories, as well as computational and numberical issues. The presentation fully illustrates the fact that the technicques of engineers, mathematicisn, and numerical analysts nicely complement each other, and they all contribute to one unified theory of structured matrices"--Back cover.

Algebraic Curves

Algebraic Curves PDF Author: Maxim E. Kazaryan
Publisher: Springer
ISBN: 3030029433
Category : Mathematics
Languages : en
Pages : 237

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Book Description
This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces. The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion. Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework