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This book provides a comprehensive introduction to some of the most significant interactions between noncommutative algebra and representation theory and classical algebraic geometry, including noncommutative projective algebraic geometry, deformation theory, symplectic reflection algebras, and noncommutative resolutions of singularities.

This book explores the connection between algebraic structures in topology and computational methods for 3-dimensional electric and magnetic field computation. Although a connection between topology and electromagnetism has been known since the 1800s, there has been very little exposition of it. This book takes steps to close that gap.

This book surveys the state-of-the-art in combinatorial game theory, that is games not involving chance or hidden information. Topics include scoring, bidding chess, Wythoff Nim, misere play, partizan bidding, loopy games, and placement games, along with a survey of temperature theory by Elwyn Berlekamp and a list of unsolved problems.

In recent years there have been many significant developments in these two fields; furthermore, the boundary between them has become increasingly blurred. Based on a series of successful lectures, this two-volume series contains survey articles and research papers by experts in the field which emphasise the connections between them. Volume 2 focuses on the most recent research.

This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 1 contains expository papers ideal for those entering the field.

This book includes a tutorial for analysing misere impartial games and how it can be used for misere partisan games. Hex and Go are featured, along with new games: Toppling Dominoes and Maze. Updated versions of Unsolved Problems in Combinatorial Game Theory and the Combinatorial Games Bibliography complete the volume.

This volume, based on the Fall 2010 MSRI program, includes review articles, research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles, and other core aspects of random matrix theory such as integrability and free probability theory.

This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics.

This volume, based on a workshop by the MSRI and addressed to both beginners and experts, offers an expository overview of the state of the art in many areas of algebraic geometry. Many chapters present approaches to long-standing open problems by means of modern techniques currently under development and contain questions and conjectures to help spur future research.

This collection of survey and research articles focuses on recent developments in quantitative aspects of 'thin groups'. It provides a broad panorama of a very active field at the boundary between geometry, dynamical systems, number theory and combinatorics for professional mathematicians and graduate students in this fascinating area of research.

This book consists of lectures that are part of the distinguished series of MSRI workshops and contains contributions by six different authors providing mathematics students and researchers with a bridge - or a window - into a portion of the intriguing world of theoretical physics, especially that which centers around Einstein gravitation and quantum field theory.

The essays in this book describe recent developments in inverse problems and imaging, including hybrid or couple-physics methods arising in medical imaging, Calderon's problem and electrical impedance tomography, inverse problems arising in global seismology and oil exploration, inverse spectral problems, and the study of asymptotically hyperbolic spaces.

An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. A system of partial differential equations, with any number of inde pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system.

From the reviews of the first edition: "This book exposes the beautiful confluence of deep techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional manifolds, compact spaces locally modeled on the world in which we live and operate...

Ihara: "Galois actions on 11"1 ( *** ) and higher circular units" * D. Ihara: "Arithmetic aspect of Galois actions on 1I"1(P - {O, 1, oo})" - survey talk * U. Matzat: - "Rationality criteria for Galois extensions" - "How to construct polynomials with Galois group Mll over Q" * B.

This volume, based on a workshop by the MSRI and addressed to both beginners and experts, offers an expository overview of the state of the art in many areas of algebraic geometry. Many chapters present approaches to long-standing open problems by means of modern techniques currently under development and contain questions and conjectures to help spur future research.

This comprehensive introduction for beginning graduate students contains articles by the leading experts in the field. It covers basic topics such as algorithmic aspects of number fields, elliptic curves, and lattice basis reduction and advanced topics including cryptography, computational class field theory, zeta functions and L-series, and quantum computing.

The three main themes of this book reflect the range of mathematical interests of Henry McKean, to whom it is dedicated. Written by experts in probability, geometry, integrable systems, turbulence, and percolation, the papers here demonstrate a variety of techniques for solving problems, often outside of the standard methods.

This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, on impartial games such as Chomp and Wythoff's Nim, and on aspects of games with infinitesimal values.

The 1992/3 academic year at the Mathematical Sciences Research Institute was devoted to Complex Algebraic Geometry. This 1996 volume collects survey articles that arose from this event, which took place at a time when algebraic geometry was undergoing a major change.

This book is based on lectures by six internationally known experts presented at the 2002 MSRI introductory workshop on commutative algebra. These focus on the interaction of commutative algebra with other areas of mathematics, including algebraic geometry, group cohomology and representation theory, and combinatorics.

Appearance of singularities is pervasive in many problems in topology, differential geometry and algebraic geometry. This book concerns the study of singular spaces using techniques from a variety of areas of geometry and topology and the interactions among them.

A collection of thirteen articles by many of the leading contributors in the field on the history of the Gross-Zagier formula and its developments. It touches on the theory of complex multiplication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, Iwasawa theory, and other topics related to the Gross-Zagier formula.

This book contains expository contributions by respected researchers on the rich combinatorial problems arising from the study of algebraic geometry, topology, commutative algebra, representation theory, and convex geometry. It will continue to be of use to graduate students and researchers in combinatorics as well as algebra, geometry, and topology.

This 2005 volume, covering a broad range of topics, is an outgrowth of the synergism of Discrete and Computational Geometry. Its surveys and research articles explore geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms, and their complexity, and the combinatorial complexity of geometric objects, particularly in low dimension.

Surveys and research articles based on a 2004 MRSI research workshop, plus a commented problem list by leading experts cover several areas of dynamical systems that have recently experienced substantial progress, including symplectic geometry; smooth rigidity; hyperbolic, parabolic, and symbolic dynamics; and ergodic theory.

The three main themes of this book reflect the range of mathematical interests of Henry McKean, to whom it is dedicated. Written by experts in probability, geometry, integrable systems, turbulence, and percolation, the papers here demonstrate a variety of techniques for solving problems, often outside of the standard methods.

First published in 2000, this expository volume of surveys and research results covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications to integrable systems.

This 1997 book contains six in-depth articles on various aspects of the field of tight and taut submanifolds and concludes with an extensive bibliography of the entire field. The first paper is an unfinished but insightful survey of the field of tight immersions and maps by Nicolaas H. Kuiper.