This book introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.
This book, which grew out of Steven Bleiler''s lecture notes from a course given by Andrew Casson at the University of Texas, is designed to serve as an introduction to the applications of hyperbolic geometry to low dimensional topology.
This book, one of the first on G2 manifolds in decades, collects introductory lectures and survey articles largely based on talks given at a workshop held at the Fields Institute in August 2017, as part of the major thematic program on geometric analysis.
Bringing together two fundamental texts from Frederic Pham's research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach.
This undergraduate and postgraduate text will familiarise readers with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations plus the means for alleviating the effects of the errors.
Configurations can be studied from a graph-theoretical viewpoint via the so-called Levi graphs and lie at the heart of graphs, groups, surfaces, and geometries, all of which are very active areas of mathematical exploration.
This second edition of Mathematical Olympiad Treasures contains a stimulating collection of problems in geometry and trigonometry, algebra, number theory, and combinatorics.
Hans Duistermaat, an influential geometer-analyst, made substantial contributions to the theory of ordinary and partial differential equations, symplectic, differential, and algebraic geometry, minimal surfaces, semisimple Lie groups, mechanics, mathematical physics, and related fields.
For the past several decades the theory of automorphic forms has become a major focal point of development in number theory and algebraic geometry, with applications in many diverse areas, including combinatorics and mathematical physics.
One of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through the theorems of Mordell, Weil, Siegel, and Faltings.
Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety.
A group of Gerry Schwarz's colleagues and collaborators gathered at the Fields Institute in Toronto for a mathematical festschrift in honor of his 60th birthday.
The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry.
by Ivor Grattan-Guinness One of the distortions in most kinds of history is an imbalance between the study devoted to major figures and to lesser ones, concerning both achievements and influence: the Great Ones may be studied to death while the others are overly ignored and thereby remain underrated.
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established.
The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics.
This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics- such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics- and in theoretical physics such as quantum field theory and string theory.
This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics.
Riemannian Topology and Geometric Structures on Manifolds results from a similarly entitled conference held at the University of New Mexico in Albuquerque.
One of the most creative mathematicians of our times, Vladimir Drinfeld received the Fields Medal in 1990 for his groundbreaking contributions to the Langlands program and to the theory of quantum groups.
