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Author: Vladimir Dragović
Publisher: Springer Science & Business Media
ISBN: 3034800150
Category : Mathematics
Languages : en
Pages : 293
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Book Description
The goal of the book is to present, in a complete and comprehensive way, areas of current research interlacing around the Poncelet porism: dynamics of integrable billiards, algebraic geometry of hyperelliptic Jacobians, and classical projective geometry of pencils of quadrics. The most important results and ideas, classical as well as modern, connected to the Poncelet theorem are presented, together with a historical overview analyzing the classical ideas and their natural generalizations. Special attention is paid to the realization of the Griffiths and Harris programme about Poncelet-type problems and addition theorems. This programme, formulated three decades ago, is aimed to understanding the higher-dimensional analogues of Poncelet problems and the realization of the synthetic approach of higher genus addition theorems.
Author: Vladimir Dragović
Publisher: Springer Science & Business Media
ISBN: 3034800150
Category : Mathematics
Languages : en
Pages : 293
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Book Description
The goal of the book is to present, in a complete and comprehensive way, areas of current research interlacing around the Poncelet porism: dynamics of integrable billiards, algebraic geometry of hyperelliptic Jacobians, and classical projective geometry of pencils of quadrics. The most important results and ideas, classical as well as modern, connected to the Poncelet theorem are presented, together with a historical overview analyzing the classical ideas and their natural generalizations. Special attention is paid to the realization of the Griffiths and Harris programme about Poncelet-type problems and addition theorems. This programme, formulated three decades ago, is aimed to understanding the higher-dimensional analogues of Poncelet problems and the realization of the synthetic approach of higher genus addition theorems.
Author: Ulrich Daepp
Publisher: American Mathematical Soc.
ISBN: 147044383X
Category : Conic sections
Languages : en
Pages : 268
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Book Description
Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Whole domains of modern mathematics have arisen from exploration of such connections--consider analytic number theory or algebraic topology. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry. The book begins with Blaschke products, complex-analytic functions that are generalizations of disk automorphisms. In the analysis of Blaschke products, we encounter, in a quite natural way, an ellipse inside the unit disk. The story continues by introducing the reader to Poncelet's theorem--a beautiful result in projective geometry that ties together two conics and, in particular, two ellipses, one circumscribed by a polygon that is inscribed in the second. The Blaschke ellipse and the Poncelet ellipse turn out to be the same ellipse, and the connection is illuminated by considering the numerical range of a $2 \times 2$ matrix. The numerical range is a convex subset of the complex plane that contains information about the geometry of the transformation represented by a matrix. Through the numerical range of $n \times n$ matrices, we learn more about the interplay between Poncelet's theorem and Blaschke products. The story ranges widely over analysis, algebra, and geometry, and the exposition of the deep and surprising connections is lucid and compelling. Written for advanced undergraduates or beginning graduate students, this book would be the perfect vehicle for an invigorating and enlightening capstone exploration. The exercises and collection of extensive projects could be used as an embarkation point for a satisfying and rich research project. You are invited to read actively using the accompanying interactive website, which allows you to visualize the concepts in the book, experiment, and develop original conjectures.
Author: Ron Donagi
Publisher: Cambridge University Press
ISBN: 1108715745
Category : Mathematics
Languages : en
Pages : 421
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Book Description
A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.
Author: Ron Donagi
Publisher: Cambridge University Press
ISBN: 110880358X
Category : Mathematics
Languages : en
Pages : 421
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Book Description
Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. This first volume covers a wide range of areas related to integrable systems, often emphasizing the deep connections with algebraic geometry. Common themes include theta functions and Abelian varieties, Lax equations, integrable hierarchies, Hamiltonian flows and difference operators. These powerful tools are applied to spinning top, Hitchin, Painleve and many other notable special equations.
Author: Frank Nijhoff
Publisher: Springer Nature
ISBN: 3030570002
Category : Mathematics
Languages : en
Pages : 240
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Book Description
This proceedings volume gathers together selected works from the 2018 “Asymptotic, Algebraic and Geometric Aspects of Integrable Systems” workshop that was held at TSIMF Yau Mathematical Sciences Center in Sanya, China, honoring Nalini Joshi on her 60th birthday. The papers cover recent advances in asymptotic, algebraic and geometric methods in the study of discrete integrable systems. The workshop brought together experts from fields such as asymptotic analysis, representation theory and geometry, creating a platform to exchange current methods, results and novel ideas. This volume's articles reflect these exchanges and can be of special interest to a diverse group of researchers and graduate students interested in learning about current results, new approaches and trends in mathematical physics, in particular those relevant to discrete integrable systems.
Author: Liang-Yee Cheng
Publisher: Springer Nature
ISBN: 3031135881
Category : Technology & Engineering
Languages : en
Pages : 1080
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Book Description
This book covers recent achievements on the ever-expanding field of Geometry and Graphics on both analogical and digital fronts, from theoretical investigations to a broad range of applications, new teaching methodologies, and historical aspects. It is from 20th International Conference on Geometry and Graphics (ICGG2022), a series of conference that started in 1978 and promoted by International Society for Geometry and Graphics, which aims to foster international collaboration and stimulate the scientific research and teaching innovations in the multidisciplinary field. The contents of the book are organized in: Theoretical Geometry and Graphics; Applied Geometry and Graphics; Engineering Computer Graphics; Graphics Education; Geometry and Graphics in History, and are intent for the academics, researchers, and professionals in architecture, engineering, industrial design, mathematics, and arts.
Author: Fritz Gesztesy
Publisher: Springer Nature
ISBN: 3030754251
Category : Mathematics
Languages : en
Pages : 388
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Book Description
The main topics of this volume, dedicated to Lance Littlejohn, are operator and spectral theory, orthogonal polynomials, combinatorics, number theory, and the various interplays of these subjects. Although the event, originally scheduled as the Baylor Analysis Fest, had to be postponed due to the pandemic, scholars from around the globe have contributed research in a broad range of mathematical fields. The collection will be of interest to both graduate students and professional mathematicians. Contributors are: G.E. Andrews, B.M. Brown, D. Damanik, M.L. Dawsey, W.D. Evans, J. Fillman, D. Frymark, A.G. García, L.G. Garza, F. Gesztesy, D. Gómez-Ullate, Y. Grandati, F.A. Grünbaum, S. Guo, M. Hunziker, A. Iserles, T.F. Jones, K. Kirsten, Y. Lee, C. Liaw, F. Marcellán, C. Markett, A. Martinez-Finkelshtein, D. McCarthy, R. Milson, D. Mitrea, I. Mitrea, M. Mitrea, G. Novello, D. Ong, K. Ono, J.L. Padgett, M.M.M. Pang, T. Poe, A. Sri Ranga, K. Schiefermayr, Q. Sheng, B. Simanek, J. Stanfill, L. Velázquez, M. Webb, J. Wilkening, I.G. Wood, M. Zinchenko.
Author: Georg Glaeser
Publisher: Springer
ISBN: 3662454505
Category : Mathematics
Languages : en
Pages : 488
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Book Description
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.
Author: Leonid Polterovich
Publisher: American Mathematical Soc.
ISBN: 147041693X
Category : Geometric function theory
Languages : en
Pages : 282
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Book Description
This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory on loop spaces gave rise to the discovery of unexpected symplectic phenomena. The present book focuses on function spaces associated with a symplectic manifold. A number of recent advances show that these spaces exhibit intriguing properties and structures, giving rise to an alternative intuition and new tools in symplectic topology. The book provides an essentially self-contained introduction into these developments along with applications to symplectic topology, algebra and geometry of symplectomorphism groups, Hamiltonian dynamics and quantum mechanics. It will appeal to researchers and students from the graduate level onwards.
Author: Marat V. Markin
Publisher: American Mathematical Society
ISBN: 1470473054
Category : Mathematics
Languages : en
Pages : 250
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Book Description
This volume contains the proceedings of the AMS-EMS-SMF Special Session on Advances in Functional Analysis and Operator Theory, held July 18–22, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The papers reflect the modern interplay between differential equations, functional analysis, operator algebras, and their applications from the dynamics to quantum groups to number theory. Among the topics discussed are the Sturm-Liouville and boundary value problems, axioms of quantum mechanics, $C^{*}$-algebras and symbolic dynamics, von Neumann algebras and low-dimensional topology, quantum permutation groups, the Jordan algebras, and the Kadison–Singer transforms.
