Algebra Geometry And Physics In The 21st Century

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Algebra, Geometry, and Physics in the 21st Century

Denis Auroux,Ludmil Katzarkov,Tony Pantev,Yan Soibelman,Yuri Tschinkel
Algebra Geometry and Physics in the 21st Century Book PDF

Author : Denis Auroux,Ludmil Katzarkov,Tony Pantev,Yan Soibelman,Yuri Tschinkel
Publisher : Birkhäuser
Page : 364 pages
File Size : 44,6 Mb
Release : 2017-07-27
Category : Mathematics
ISBN : 9783319599397

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Algebra, Geometry, and Physics in the 21st Century by Denis Auroux,Ludmil Katzarkov,Tony Pantev,Yan Soibelman,Yuri Tschinkel Pdf

This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim’s vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over finite fields, and has brought forth a paradigm shift at the interface of modern geometry and mathematical physics. Many of his papers have opened completely new directions of research and led to the solutions of many classical problems. This book collects papers by leading experts currently engaged in research on topics close to Maxim’s heart. Contributors: S. Donaldson A. Goncharov D. Kaledin M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren

Foundations of Mathematics and Physics One Century After Hilbert

Joseph Kouneiher
Foundations of Mathematics and Physics One Century After Hilbert Book PDF

Author : Joseph Kouneiher
Publisher : Springer
Page : 441 pages
File Size : 40,8 Mb
Release : 2018-05-26
Category : Science
ISBN : 9783319648132

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Foundations of Mathematics and Physics One Century After Hilbert by Joseph Kouneiher Pdf

This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert’s works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, but sheds light on future developments of the field, highlighting a list of open problems. Graduate students and researchers working in physics, mathematics and mathematical physics will find this journey extremely fascinating. All those who want to benefit from a comprehensive description of all the latest advances in mathematics and mathematical physics, will find this book very useful too.

Advances in Algebraic Geometry Motivated by Physics

Emma Previato
Advances in Algebraic Geometry Motivated by Physics Book PDF

Author : Emma Previato
Publisher : American Mathematical Soc.
Page : 310 pages
File Size : 41,7 Mb
Release : 2001
Category : Geometry, Algebraic
ISBN : 9780821828106

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Advances in Algebraic Geometry Motivated by Physics by Emma Previato Pdf

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.

New Trends in Geometry

Claudio Bartocci,Luciano Boi,Corrado Sinigaglia
New Trends in Geometry Book PDF

Author : Claudio Bartocci,Luciano Boi,Corrado Sinigaglia
Publisher : World Scientific
Page : 329 pages
File Size : 47,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9781848166424

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New Trends in Geometry by Claudio Bartocci,Luciano Boi,Corrado Sinigaglia Pdf

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.

Mathematics And The 21st Century - Proceedings Of The International Conference

A A Ashour,A-s F Obada
Mathematics And The 21st Century Proceedings Of The International Conference Book PDF

Author : A A Ashour,A-s F Obada
Publisher : World Scientific
Page : 412 pages
File Size : 46,7 Mb
Release : 2001-04-02
Category : Mathematics
ISBN : 9789814491587

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Mathematics And The 21st Century - Proceedings Of The International Conference by A A Ashour,A-s F Obada Pdf

Contents:Millennium Lecture — Cairo, 15 January 2000 (M Atiyah)Trends for Science and Mathematics in the 21st Century (P A Griffiths)Arabic Mathematics and Rewriting the History of Mathematics (R Rashed)The Paradigm Shift in Mathematics Education: A Scenario for Change (W Ebeid)Einstein's Theory of Spacetime and Gravity (J Ehlers)Moduli Problems in Geometry (M S Narasimhan)Enumerative Geometry from the Greeks to Strings (C Procesi)Optical Solitons: Twenty-Seven Years of the Last Millennium and Three More Years of the New? (R K Bullough)Concepts of Non-Smooth Dynamical Systems (T Küpper)Radical Theory: Developments and Trends (R Wiegandt)On Minimal Subgroups of Finite Groups (M Asaad)Totally and Mutually Permutable Products of Finite Groups (A Ballester-Bolinches)Asymptotic Behaviour of Solutions of Evolution Equations (B Basit)On Nonlinear Evolution Equations with Applications (L Debnath)A Robust Layer-Resolving Numerical Method for a Free Convection Problem (J Étienne et al.)Growth Value-Distribution and Zero-Free Regions of Entire Functions and Sections (F F Abi-Khuzam)Three Linear Preserver Problems (A R Sourour)Prediction: Advances and New Research (E K Al-Hussaini)Inference on Parameters of the Laplace Distribution Based on Type-II Censored Samples Using Edgeworth Approximation (N Balakrishnan et al.)Mathematical Models in the Theory of Accelerated Experiments (V Bagdonavicius & M Nikulin)The Vibrations of a Drum with Fractal Boundary (J Fleckinger-Pellé)Intermediate States: Some Nonclassical Properties (M S Abdalla & A-S F Obada)On the Relativistic Two-Body Equation (S R Komy)Singularities in General Relativity and the Origin of Charge (K Buchner)The Inner Geometry of Light Cone in Godel Universe (M Abdel-Megied) Readership: Mathematicians. Keywords:Proceedings;Conference;Mathematics;Cairo (Egypt)

Mathematics and the 21st Century

A. A. Ashour,A. -S. F. Obada
Mathematics and the 21st Century Book PDF

Author : A. A. Ashour,A. -S. F. Obada
Publisher : World Scientific
Page : 412 pages
File Size : 40,9 Mb
Release : 2001
Category : Mathematics
ISBN : 9789810245481

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Mathematics and the 21st Century by A. A. Ashour,A. -S. F. Obada Pdf

http://www.worldscientific.com/worldscibooks/10.1142/4633

The Orbit Method in Geometry and Physics

Aleksandr Aleksandrovich Kirillov,Christian Duval,Laurent Guieu,Valentin Ovsienko
The Orbit Method in Geometry and Physics Book PDF

Author : Aleksandr Aleksandrovich Kirillov,Christian Duval,Laurent Guieu,Valentin Ovsienko
Publisher : Springer Science & Business Media
Page : 518 pages
File Size : 49,9 Mb
Release : 2003-05-15
Category : Mathematics
ISBN : 0817642323

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The Orbit Method in Geometry and Physics by Aleksandr Aleksandrovich Kirillov,Christian Duval,Laurent Guieu,Valentin Ovsienko Pdf

The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and remains a useful and powerful tool in such areas as Lie theory, representation theory, integrable systems, complex geometry, and mathematical physics. Among the distinguished names associated with the orbit method is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962), places him as the founder of orbit theory. The original research papers in this volume are written by prominent mathematicians and reflect recent achievements in orbit theory and other closely related areas such as harmonic analysis, classical representation theory, Lie superalgebras, Poisson geometry, and quantization. Contributors: A. Alekseev, J. Alev, V. Baranovksy, R. Brylinski, J. Dixmier, S. Evens, D.R. Farkas, V. Ginzburg, V. Gorbounov, P. Grozman, E. Gutkin, A. Joseph, D. Kazhdan, A.A. Kirillov, B. Kostant, D. Leites, F. Malikov, A. Melnikov, P.W. Michor, Y.A. Neretin, A. Okounkov, G. Olshanski, F. Petrov, A. Polishchuk, W. Rossmann, A. Sergeev, V. Schechtman, I. Shchepochkina. The work will be an invaluable reference for researchers in the above mentioned fields, as well as a useful text for graduate seminars and courses.

Topics in Physical Mathematics

Kishore Marathe
Topics in Physical Mathematics Book PDF

Author : Kishore Marathe
Publisher : Springer Science & Business Media
Page : 458 pages
File Size : 51,9 Mb
Release : 2010-08-09
Category : Mathematics
ISBN : 9781848829398

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Topics in Physical Mathematics by Kishore Marathe Pdf

As many readers will know, the 20th century was a time when the fields of mathematics and the sciences were seen as two separate entities. Caused by the rapid growth of the physical sciences and an increasing abstraction in mathematical research, each party, physicists and mathematicians alike, suffered a misconception; not only of the opposition’s theoretical underpinning, but of how the two subjects could be intertwined and effectively utilized. One sub-discipline that played a part in the union of the two subjects is Theoretical Physics. Breaking it down further came the fundamental theories, Relativity and Quantum theory, and later on Yang-Mills theory. Other areas to emerge in this area are those derived from the works of Donaldson, Chern-Simons, Floer-Fukaya, and Seiberg-Witten. Aimed at a wide audience, Physical Topics in Mathematics demonstrates how various physical theories have played a crucial role in the developments of Mathematics and in particular, Geometric Topology. Issues are studied in great detail, and the book steadfastly covers the background of both Mathematics and Theoretical Physics in an effort to bring the reader to a deeper understanding of their interaction. Whilst the world of Theoretical Physics and Mathematics is boundless; it is not the intention of this book to cover its enormity. Instead, it seeks to lead the reader through the world of Physical Mathematics; leaving them with a choice of which realm they wish to visit next.

Algebraic Curves

Maxim E. Kazaryan,Sergei K. Lando,Victor V. Prasolov
Algebraic Curves Book PDF

Author : Maxim E. Kazaryan,Sergei K. Lando,Victor V. Prasolov
Publisher : Springer
Page : 231 pages
File Size : 43,6 Mb
Release : 2019-01-21
Category : Mathematics
ISBN : 9783030029432

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Algebraic Curves by Maxim E. Kazaryan,Sergei K. Lando,Victor V. Prasolov Pdf

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

The Universe of Conics

Georg Glaeser,Hellmuth Stachel,Boris Odehnal
The Universe of Conics Book PDF

Author : Georg Glaeser,Hellmuth Stachel,Boris Odehnal
Publisher : Springer
Page : 488 pages
File Size : 55,7 Mb
Release : 2016-03-22
Category : Mathematics
ISBN : 9783662454503

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The Universe of Conics by Georg Glaeser,Hellmuth Stachel,Boris Odehnal Pdf

This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to derive projective, affine and metrical properties, covering both Euclidean and non-Euclidean geometries. With more than two thousand years of history, conic sections play a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics. This text will be invaluable to undergraduate mathematics students, those in adjacent fields of study, and anyone with an interest in classical geometry. Augmented with more than three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises.

Tales of Mathematicians and Physicists

Simon Gindikin
Tales of Mathematicians and Physicists Book PDF

Author : Simon Gindikin
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 41,9 Mb
Release : 2007-04-26
Category : Mathematics
ISBN : 9780387488110

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Tales of Mathematicians and Physicists by Simon Gindikin Pdf

This revised and greatly expanded second edition of the Russian text contains a wealth of new information about the lives and accomplishments of more than a dozen scientists throughout five centuries of history: from the first steps in algebra up to new achievements in geometry in connection with physics. The heroes of the book are renowned figures from early eras, as well some scientists of last century. A unique mixture of mathematics, physics, and history, this volume provides biographical glimpses of scientists and their contributions in the context of the social and political background of their times.

Mathematical Models In Science

Olav Arnfinn Laudal
Mathematical Models In Science Book PDF

Author : Olav Arnfinn Laudal
Publisher : World Scientific
Page : 319 pages
File Size : 46,9 Mb
Release : 2021-06-16
Category : Science
ISBN : 9781800610293

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Mathematical Models In Science by Olav Arnfinn Laudal Pdf

Mathematical Models in Science treats General Relativity and Quantum Mechanics in a non-commutative Algebraic Geometric framework.Based on ideas first published in Geometry of Time-Spaces: Non-commutative Algebraic Geometry Applied to Quantum Theory (World Scientific, 2011), Olav Arnfinn Laudal proposes a Toy Model as a Theory of Everything, starting with the notion of the Big Bang in Cosmology, modeled as the non-commutative deformation of a thick point. From this point, the author shows how to extract reasonable models for both General Relativity and Quantum Theory. This book concludes that the universe turns out to be the 6-dimensional Hilbert scheme of pairs of points in affine 3-space. With this in place, one may develop within the model much of the physics known to the reader. In particular, this theory is applicable to the concept of Dark Matter and its effects on our visual universe.Hence, Mathematical Models in Science proves the dependency of deformation theory in Mathematical Physics and summarizes the development of physical applications of pure mathematics developed in the twentieth century.

The Orbit Method in Geometry and Physics

Christian Duval,Laurent Guieu,Valentin Ovsienko
The Orbit Method in Geometry and Physics Book PDF

Author : Christian Duval,Laurent Guieu,Valentin Ovsienko
Publisher : Birkhäuser
Page : 474 pages
File Size : 48,8 Mb
Release : 2013-10-03
Category : Mathematics
ISBN : 1461265800

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The Orbit Method in Geometry and Physics by Christian Duval,Laurent Guieu,Valentin Ovsienko Pdf

The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and remains a useful and powerful tool in such areas as Lie theory, representation theory, integrable systems, complex geometry, and mathematical physics. Among the distinguished names associated with the orbit method is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962), places him as the founder of orbit theory. The original research papers in this volume are written by prominent mathematicians and reflect recent achievements in orbit theory and other closely related areas such as harmonic analysis, classical representation theory, Lie superalgebras, Poisson geometry, and quantization. Contributors: A. Alekseev, J. Alev, V. Baranovksy, R. Brylinski, J. Dixmier, S. Evens, D.R. Farkas, V. Ginzburg, V. Gorbounov, P. Grozman, E. Gutkin, A. Joseph, D. Kazhdan, A.A. Kirillov, B. Kostant, D. Leites, F. Malikov, A. Melnikov, P.W. Michor, Y.A. Neretin, A. Okounkov, G. Olshanski, F. Petrov, A. Polishchuk, W. Rossmann, A. Sergeev, V. Schechtman, I. Shchepochkina. The work will be an invaluable reference for researchers in the above mentioned fields, as well as a useful text for graduate seminars and courses.

Real Algebraic Geometry

Vladimir I. Arnold
Real Algebraic Geometry Book PDF

Author : Vladimir I. Arnold
Publisher : Springer Science & Business Media
Page : 113 pages
File Size : 44,6 Mb
Release : 2013-04-15
Category : Mathematics
ISBN : 9783642362439

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Real Algebraic Geometry by Vladimir I. Arnold Pdf

This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images. At one of the first international mathematical congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the nineteenth century as a legacy for the twentieth century). In spite of the simplicity and importance of this problem (including its numerous applications), it remains unsolved to this day (although, as you will now see, many remarkable results have been discovered).

Geometry and Theoretical Physics

Joachim Debrus,Allen C. Hirshfeld
Geometry and Theoretical Physics Book PDF

Author : Joachim Debrus,Allen C. Hirshfeld
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642763533

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Geometry and Theoretical Physics by Joachim Debrus,Allen C. Hirshfeld Pdf

The interaction between geometry and theoretical physics has often been very fruitful. A highlight in this century was Einstein's creation of the theory of general relativity. Equally impressive was the recognition, starting from the work of Yang and Mills and culminating in the Weinberg-Salam theory of the electroweak interaction and quantum chromodynamics, that the fundamental interactions of elementary particles are governed by gauge fields, which in ma thematical terms are connections in principal fibre bundles. Theoretical physi cists became increasingly aware of the fact that the use of modern mathematical methods may be necessary in the treatment of problems of physical interest. Since some of these topics are covered at most summarily in the usual curricu lum, there is a need for extra-curricular efforts to provide an opportunity for learning these techniques and their physical applications. In this context we arranged a meeting at the Physikzentrum Bad Ronnef 12-16 February 1990 on the subject "Geometry and Theoretical Physics", in the series of physics schools organized by the German Physical Society. The participants were graduate students from German universities and research institutes. Since the meeting occurred only a short time after freedom of travel between East and West Germany became a reality, this was for many from the East the first opportunity to attend a scientific meeting in the West, and for many from the West the first chance to become personally acquainted with colleagues from the East.