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Addressing physicists and mathematicians alike, this book discusses the finite dimensional representation theory of sl(2), both classical and quantum. Covering representations of U(sl(2)), quantum sl(2), the quantum trace and color representations, and the Turaev-Viro invariant, it is useful to graduate students and professionals.

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Discusses the symmetric, linear, orthogonal, and symplectic groups and determines their invariants and representations. This book covers topics such as matrix algebras, semigroups, commutators, and spinors, which help in understanding the group-theoretic structure of quantum mechanics.

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Scholars in various fields are exploring similar ideas to combat indeterminism when conditions seem chaotic and prohibit the use of a rigid program approach, even with probabilities.

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Addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies.

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Requiring no more background than plane geometry and elementary algebra, this book leads the reader into some of the most fundamental ideas of mathematics, the ideas that make the subject exciting and interesting.

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What is so special about the number 30 How many colors are needed to color a map Do the prime numbers go on forever Are there more whole numbers than even numbers These and other mathematical puzzles are explored in this delightful book by two eminent mathematicians. Requiring no more background than plane geometry and elementary algebra, this

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Develops a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. This book formulates simple general conditions on the spectral theory of the group and the regularity of the averaging sets, which suffice to guarantee convergence to the ergodic mean.

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When John Nash won the Nobel prize in economics in 1994, many people were surprised to learn that he was alive. This book presents Nash's contributions not only to game theory, for which he received the Nobel, but to mathematics - from Riemannian geometry and partial differential equations - in which he commands greater acclaim among academics.

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The problem of how to estimate probabilities has interested philosophers, statisticians, actuaries, and mathematicians for a long time. It is currently of interest for automatic recognition, medical diagnosis, and artificial intelligence in general. This monograph reviews existing methods, including those that are new or have not been written up in a connected manner.

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Providing instances of the local Langlands conjecture, this book aims to prove the local Langlands conjecture for GLn over a p-adic field and, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieties.

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Systems governed by non-linear differential equations are of fundamental importance in all branches of science, but our understanding of them is still extremely limited. In this book a particular system, describing the interaction of magnetic monopoles, is investigated in detail. The use of new geometrical methods produces a reasonably clear pictur

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The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singul

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Offers a comprehensive account of the Gross-Zagier formula on Shimura curves over real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. This title begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations.

(Hardback)

Offers a comprehensive account of the Gross-Zagier formula on Shimura curves over real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. This title begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations.

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Presents the analytic foundations to the theory of the hypoelliptic Laplacian. This book shows that the hypoelliptic Laplacian provides a geometric version of the Fokker-Planck equations. It gives the proper functional analytic setting in order to study this operator and develop a pseudodifferential calculus.

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A semantically well-defined programming language widely used in artificial intelligence, Prolog has greatly influenced other programming languages since its introduction in the late 1970s. A user may find Prolog deceptively easy, however, and there are a number of different implementations. In this book Patrice Boizumault draws from his extensive e

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The story of the man who introduced Hindu-Arabic numerals and the concept of zero to Europe that transformed business in the late Middle Ages and paved the way for the commercial and cultural explosion of the Renaissance

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This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population.

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A fascinating look at how mathematics has influenced human civilization and evolution throughout history.