Geometry

One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems.

Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade.

The original goal that ultimately led to this volume was the construction of "e;motivic cohomology theory,"e; whose existence was conjectured by A.

This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it.

Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place.

This book studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q.

This book presents the analytic foundations to the theory of the hypoelliptic Laplacian.

Outer billiards is a basic dynamical system defined relative to a convex shape in the plane.

Resolution of singularities is a powerful and frequently used tool in algebraic geometry.

For hundreds of years, the study of elliptic curves has played a central role in mathematics.

Between the seventeenth and nineteenth centuries Japan was totally isolated from the West by imperial decree.

A foundational account of a new construction in the p-adic Langlands correspondenceMotivated by the p-adic Langlands program, this book constructs stacks that algebraize Mazur's formal deformation rings of local Galois representations.

New mathematical research in arithmetic dynamicsIn The Arithmetic of Polynomial Dynamical Pairs, Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics.

A fascinating exploration of the pentagon and its role in various culturesThe pentagon and its close cousin, the pentagram, have inspired individuals for the last two and half millennia, from mathematicians and philosophers to artists and naturalists.

These notes are based on a course of lectures given at Princeton University during the academic year 19661967.

This book is the first to present a new area of mathematical research that combines topology, geometry, and logic.

This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology.

These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant theory associates to reductive group actions on nonsingular complex projective varieties.

Essential mathematical insights into one of the most important and challenging open problems in general relativity-the stability of black holesOne of the major outstanding questions about black holes is whether they remain stable when subject to small perturbations.

Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry.

Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples.

This book presents the complete proof of the Bloch-Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry.

This book studies the interplay between the geometry and topology of locally symmetric spaces, and the arithmetic aspects of the special values of L-functions.

Differential Equations on Fractals opens the door to understanding the recently developed area of analysis on fractals, focusing on the construction of a Laplacian on the Sierpinski gasket and related fractals.

An advanced treatment of surgery theory for graduate students and researchersSurgery theory, a subfield of geometric topology, is the study of the classifications of manifolds.

A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K.

An exploration of mathematical style through 99 different proofs of the same theoremThis book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem.

Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion.

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments.

An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentiethThe Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s.

An inviting, intuitive, and visual exploration of differential geometry and formsVisual Differential Geometry and Forms fulfills two principal goals.

This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology.

John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P.

How mathematics helped build the world's most important buildings from early Egypt to the presentFrom the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings.

An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group.

This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology.

This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography.

William Thurston (1946-2012) was one of the great mathematicians of the twentieth century.

Los Elementos de Euclides es una de las escasisimas obras antiguas que puede presumir de haber constituido, casi de golpe, la base sobre la que se ha levantado toda una ciencia, en este caso la geometria y la aritmetica, al menos desde el siglo III a.

Los Elementos de Euclides es una de las escasisimas obras antiguas que puede presumir de haber constituido, casi de golpe, la base sobre la que se ha levantado toda una ciencia, en este caso la geometria y la aritmetica, al menos desde el siglo III a.

Este es un libro producto de la revision bibliografica y la reflexion personal como docentes de geometria euclidiana, surgio la necesidad de plantear una unidad didactica basada en el planteamiento y la resolucion de problemas que promuevan el desarrollo del razonamiento geometrico en estudiantes de educacion superior, especialmente del curso de geometria euclidiana.

Los temas matematicos tratados en estos trabajos no son, por supuesto, nada nuevo para quien haya estudiado con cierta dedicacion la Matematica de bachillerato.

Desde tiempos del cardenal Richelieu, cuando entre las habilidades de un mosquetero se incluia el saber jugar billar, hasta las peliculas como The Hustler y The Colour of Money, el billar siempre ha fascinado por su combinacion de juego y ciencia.

Esta obra presenta un estudio detallado y riguroso, en el que se hace uso de herramientas del álgebra lineal (matrices, valores y vectores propios, el teorema espectral, para matrices simétricas) que permiten identificar y reducir los lugares geométricos representados por la ecuación general de segundo grado en dos variables (las cónicas) y en tres variables (las superficies cuádricas).

Este libro tiene como objetivos:1) Introducción a los métodos modernos de cálculo de estructuras.

Este libro constituye el cuarto volumen de la serie "Matemáticas para Ingeniería", que se centra en el álgebra lineal y la geometría vectorial.

Este libro es el primero de la colección "Matemáticas para Ingeniería", que se centra en el aprendizaje y consolidación de los conocimientos matemáticos previos necesarios para todo estudiante de ingeniería de la PUCV.

Geometría diferencial de curvas y superficies es un texto dirigido a estudiantes de educación superior, que estén empezando su ciclo de profesionalización en programas académicos de ciencias e ingenierías, y que tengan conocimientos previos de cálculo en varias variables y álgebra lineal; y se enfoca más en aspectos geométricos que en aspectos de análisis o de topología, con el objetivo de desarrollar en el estudiante su intuición geométrica.

Esta cartilla recopila los conceptos basicos y necesarios para abordar los primeros cursos de matematicas a nivel superior, a saber: las operaciones con numeros reales y sus respectivas propiedades,en particular, se dedica un capitulo exclusivo a la potenciacion, radicacion y logaritmacion, las cuales se presentan en forma comparativa, de este modo el lector puede visualizar como se relacionan y diferencian entre ellas.

This book uses the genre of philosophy to approach a conceptual truth which is inherent in human nature; that is 'dimensional simplification'.