Algebra, Geometry, and Physics in the 21st Century
Algebra, Geometry, and Physics in the 21st Century

Author: Denis Auroux

Publisher: Birkhäuser

Published: 2017-07-27

Total Pages: 368

ISBN-13: 3319599399

DOWNLOAD EBOOK

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

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

Author: A A Ashour

Publisher: World Scientific

Published: 2001-04-02

Total Pages: 412

ISBN-13: 9814491586

DOWNLOAD EBOOK

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)

Foundations of Mathematics and Physics One Century After Hilbert
Foundations of Mathematics and Physics One Century After Hilbert

Author: Joseph Kouneiher

Publisher: Springer

Published: 2018-05-26

Total Pages: 454

ISBN-13: 3319648136

DOWNLOAD EBOOK

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.

New Trends in Geometry
New Trends in Geometry

Author: Luciano Boi

Publisher: World Scientific

Published: 2011

Total Pages: 329

ISBN-13: 1848166435

DOWNLOAD EBOOK

This volume focuses on the interactions between mathematics, physics, biology and neuroscience by exploring new geometrical and topological modelling 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, as well as molecular and cell biology and the neurosciences, will constitute the new frontier of 21st century science, where breakthroughs are more likely to span across traditional disciplines.

Advances in Algebraic Geometry Motivated by Physics
Advances in Algebraic Geometry Motivated by Physics

Author: Emma Previato

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 310

ISBN-13: 082182810X

DOWNLOAD EBOOK

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.

Mathematics Into the Twenty-first Century
Mathematics Into the Twenty-first Century

Author: American Mathematical Society

Publisher: American Mathematical Soc.

Published: 1992

Total Pages: 514

ISBN-13: 9780821801673

DOWNLOAD EBOOK

In the summer of 1988 in Providence, the AMS celebrated its centennial with a wide range of mathematical activities. Among those was a symposium, Mathematics into the Twenty-first Century, which brought together a number of the top research mathematicians who will likely have a significant impact on the mathematics of this century. This book contains the lectures presented by 16 of the 18 individuals who spoke during the symposium. Written by some of the major international figures in mathematical research, this group of articles covers a panorama of the vital areas of mathematics at the turn of the 21st century and gives the general mathematical reader a broad perspective on some of the major trends in research.

Sheaves on Manifolds
Sheaves on Manifolds

Author: Masaki Kashiwara

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 522

ISBN-13: 3662026619

DOWNLOAD EBOOK

Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view. From the reviews: "Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." –Bulletin of the L.M.S.

Curvature in Mathematics and Physics
Curvature in Mathematics and Physics

Author: Shlomo Sternberg

Publisher: Courier Corporation

Published: 2013-04-17

Total Pages: 418

ISBN-13: 0486292711

DOWNLOAD EBOOK

Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.

Geometry and Theoretical Physics
Geometry and Theoretical Physics

Author: Joachim Debrus

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 333

ISBN-13: 3642763537

DOWNLOAD EBOOK

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.

Algebra, Geometry and Mathematical Physics
Algebra, Geometry and Mathematical Physics

Author: Abdenacer Makhlouf

Publisher: Springer

Published: 2014-06-17

Total Pages: 680

ISBN-13: 3642553613

DOWNLOAD EBOOK

This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers and advanced students.