A Celebration of John F. Nash Jr.

A Celebration of John F. Nash Jr.
Author: Harold W. Kuhn
Publisher: Duke University Press
Total Pages: 512
Release: 1996
Genre: Business & Economics
ISBN: 9780822317821

This collection celebrates the pathbreaking work in game theory and mathematics of John F. Nash Jr., winner of the 1994 Nobel Prize in Economics. Nash's analysis of equilibria in the theory of non-cooperative games has had a major impact on modern economic theory. This book, also published as volume 81 of the Duke Mathematical Journal, includes an important, but previously unpublished paper by Nash; the proceedings of the Nobel seminar held in Stockholm on December 8, 1994 in his honor; and papers by distinguished mathematicians and economists written in response to and in honor of Nash's pioneering contributions to those fields. In 1950, when he was 22 years old, Nash presented his key idea--the Nash equilibrium--in the Ph.D. thesis he submitted to the Mathematics Department at Princeton University. In that paper, he defined a new concept of equilibrium and used methods from topology to prove the existence of an equilibrium point for n-person, finite, non-cooperative games, that is, for games in which the number of possible strategies are limited, no communication is allowed between the players, and n represents the number of players. The Nash equilibrium point is reached when none of the players can improve their position by changing strategies. By taking into account situations involving more than two players, specifically the general n-player game, Nash built significantly on the previous work of John Von Neumann and Oskar Morgenstern. Contributors. Abbas Bahri, Eric A. Carlen, Ennio De Giorgi, Charles Fefferman, Srihari Govidan, John C. Harsanyi, H. Hoffer, Carlos E. Kenig, S. Klainerman, Harold F. Kuhn, Michael Loss, William F. Lucas, M. Machedon, Roger B. Myerson, Raghavan Narasimhan, John F. Nash Jr., Louis Nirenberg, Jill Pipher, Zeév Rudnick, Peter Sarnak, Michael Shub, Steve Smale, Robert Wilson, K. Wysocki, E. Zehnder

Open Problems in Mathematics

Open Problems in Mathematics
Author: John Forbes Nash, Jr.
Publisher: Springer
Total Pages: 543
Release: 2018-05-31
Genre: Mathematics
ISBN: 9783319812106

The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.

The Essential John Nash

The Essential John Nash
Author: John Nash
Publisher: Princeton University Press
Total Pages: 273
Release: 2016-06-29
Genre: Mathematics
ISBN: 140088408X

When John Nash won the Nobel prize in economics in 1994, many people were surprised to learn that he was alive and well. Since then, Sylvia Nasar's celebrated biography A Beautiful Mind, the basis of a new major motion picture, has revealed the man. The Essential John Nash reveals his work--in his own words. This book presents, for the first time, the full range of Nash's diverse contributions not only to game theory, for which he received the Nobel, but to pure mathematics--from Riemannian geometry and partial differential equations--in which he commands even greater acclaim among academics. Included are nine of Nash's most influential papers, most of them written over the decade beginning in 1949. From 1959 until his astonishing remission three decades later, the man behind the concepts "Nash equilibrium" and "Nash bargaining"--concepts that today pervade not only economics but nuclear strategy and contract talks in major league sports--had lived in the shadow of a condition diagnosed as paranoid schizophrenia. In the introduction to this book, Nasar recounts how Nash had, by the age of thirty, gone from being a wunderkind at Princeton and a rising mathematical star at MIT to the depths of mental illness. In his preface, Harold Kuhn offers personal insights on his longtime friend and colleague; and in introductions to several of Nash's papers, he provides scholarly context. In an afterword, Nash describes his current work, and he discusses an error in one of his papers. A photo essay chronicles Nash's career from his student days in Princeton to the present. Also included are Nash's Nobel citation and autobiography. The Essential John Nash makes it plain why one of Nash's colleagues termed his style of intellectual inquiry as "like lightning striking." All those inspired by Nash's dazzling ideas will welcome this unprecedented opportunity to trace these ideas back to the exceptional mind they came from.

Mathematics and Culture I

Mathematics and Culture I
Author: Michele Emmer
Publisher: Springer Science & Business Media
Total Pages: 372
Release: 2003-12-02
Genre: Science
ISBN: 9783540017707

A fascinating and insightful collection of papers on the strong links between mathematics and culture. The contributions range from cinema and theatre directors to musicians, architects, historians, physicians, graphic designers and writers. The text highlights the cultural and formative character of mathematics, its educational value, and imaginative dimension. These articles are highly interesting, sometimes amusing, and make excellent starting points for researching the strong connection between scientific and literary culture.

The Grand Canyon: Unseen Beauty

The Grand Canyon: Unseen Beauty
Author: Thomas Blagden Jr.
Publisher: Rizzoli Publications
Total Pages: 0
Release: 2021-10-12
Genre: Travel
ISBN: 0789341115

The majesty of the Grand Canyon is celebrated from the Colorado River as it continues to carve America's natural wonder from a mile below the rim. As one of the Wonders of the World and the most iconic national park in America, the Grand Canyon enthralls six million visitors each year. Only a small fraction of those people, however, have the privilege of experiencing the canyon by rafting down the Colorado River. The Grand Canyon captures and evokes the power of that journey from the drama of the rapids and the immeasurable scale of the canyon walls to the subtle rock patterns and varied life forms. What started as an exceptional opportunity for Tom Blagden to raft through The Canyon in 2006 with Rod Nash at the oars has evolved into a passionate photographic pursuit that still continues. The route--the River--is the same every time but the experience constantly variable and deeply profound. Rafters never tire of it and, if anything, feel more in awe of the Canyon's magnificence with each trip. Tom Blagden's images and Rod Nash's essay reveal the canyon from a different perspective portraying what it's like to be on the river and immersed a mile deep, surrounded by rock almost half the age of the earth. On the centennial of Grand Canyon National Park it seems only fitting that we journey together to this unique place through the pages of this astonishing book. The book weaves a wondrous adventure that will bring readers along on a journey while raising questions about the significance of a national park and an iconic American river and how to sustain them for generations to follow.

Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1

Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1
Author: Raf Cluckers
Publisher: Cambridge University Press
Total Pages: 347
Release: 2011-09-22
Genre: Mathematics
ISBN: 1139499793

Assembles different theories of motivic integration for the first time, providing all of the necessary background for graduate students and researchers from algebraic geometry, model theory and number theory. In a rapidly-evolving area of research, this volume and Volume 2, which unite the several viewpoints and applications, will prove invaluable.

Arc Schemes And Singularities

Arc Schemes And Singularities
Author: David Bourqui
Publisher: World Scientific
Total Pages: 312
Release: 2020-03-05
Genre: Mathematics
ISBN: 1786347210

This title introduces the theory of arc schemes in algebraic geometry and singularity theory, with special emphasis on recent developments around the Nash problem for surfaces. The main challenges are to understand the global and local structure of arc schemes, and how they relate to the nature of the singularities on the variety. Since the arc scheme is an infinite dimensional object, new tools need to be developed to give a precise meaning to the notion of a singular point of the arc scheme.Other related topics are also explored, including motivic integration and dual intersection complexes of resolutions of singularities. Written by leading international experts, it offers a broad overview of different applications of arc schemes in algebraic geometry, singularity theory and representation theory.

Model Theory, Algebra, and Geometry

Model Theory, Algebra, and Geometry
Author: Deirdre Haskell
Publisher: Cambridge University Press
Total Pages: 244
Release: 2000-07-03
Genre: Mathematics
ISBN: 9780521780681

Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.

Motivic Integration

Motivic Integration
Author: Antoine Chambert-Loir
Publisher: Springer
Total Pages: 526
Release: 2018-09-15
Genre: Mathematics
ISBN: 149397887X

This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties. This theory is rooted in a groundbreaking idea of Kontsevich and was further developed by Denef & Loeser and Sebag. It is presented in the context of formal schemes over a discrete valuation ring, without any restriction on the residue characteristic. The text first discusses the main features of the Grothendieck ring of varieties, arc schemes, and Greenberg schemes. It then moves on to motivic integration and its applications to birational geometry and non-Archimedean geometry. Also included in the work is a prologue on p-adic analytic manifolds, which served as a model for motivic integration. With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration. It will also serve as a motivation for more recent and sophisticated theories that have been developed since.