This open access book covers the main topics for a course on the differential geometry of curves and surfaces. Unlike the common approach in existing textbooks, there is a strong focus on variationa……続きを見る
The content in Chapter 1-3 is a fairly standard one-semester course on local rings with the goal to reach the fact that a regular local ring is a unique factorization domain. The homological machine……続きを見る
Discriminant equations are an important class of Diophantine equations with close ties to algebraic number theory, Diophantine approximation and Diophantine geometry. This book is the first comprehe……続きを見る
Pencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP². Especially how it is the data describing the mutu……続きを見る
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a co……続きを見る
Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to t……続きを見る
This book offers a review of the vibrant areas of geometric representation theory and gauge theory, which are characterized by a merging of traditional techniques in representation theory with the u……続きを見る
This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry. Authored by leading experts in their fields, the l……続きを見る
This book presents recent advances on Kobayashi hyperbolicity in complex geometry, especially in connection with projective hypersurfaces. This is a very active field, not least because of the fasci……続きを見る
The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in ……続きを見る
This is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry. It examines bodies of constant width from sever……続きを見る
The main aim of this book is to present several results related to functions of unitary operators on complex Hilbert spaces obtained, by the author in a sequence of recent research papers. The funda……続きを見る
Carl Friedrich Gauss, the "foremost of mathematicians," was a land surveyor. Measuring and calculating geodetic networks on the curved Earth was the inspiration for some of his greatest mathematical……続きを見る
Collecting together the lecture notes of the CIME Summer School held in Cetraro in July 2018, the aim of the book is to introduce a vast range of techniques which are useful in the investigation of ……続きを見る
Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which……続きを見る
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing an o……続きを見る
