Surveys In Geometry I
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Author | : Athanase Papadopoulos |
Publisher | : Springer Nature |
Total Pages | : 469 |
Release | : 2022-02-18 |
Genre | : Mathematics |
ISBN | : 3030866955 |
The volume consists of a set of surveys on geometry in the broad sense. The goal is to present a certain number of research topics in a non-technical and appealing manner. The topics surveyed include spherical geometry, the geometry of finite-dimensional normed spaces, metric geometry (Bishop—Gromov type inequalities in Gromov-hyperbolic spaces), convexity theory and inequalities involving volumes and mixed volumes of convex bodies, 4-dimensional topology, Teichmüller spaces and mapping class groups actions, translation surfaces and their dynamics, and complex higher-dimensional geometry. Several chapters are based on lectures given by their authors to middle-advanced level students and young researchers. The whole book is intended to be an introduction to current research trends in geometry.
Author | : Izzet Coskun |
Publisher | : American Mathematical Soc. |
Total Pages | : 386 |
Release | : 2017-07-12 |
Genre | : Mathematics |
ISBN | : 1470435578 |
The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.
Author | : Claude LeBrun |
Publisher | : American Mathematical Society(RI) |
Total Pages | : 450 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : |
This is the sixth volume in a series providing surveys of differential geometry. It addresses: Einstein manifolds with zero Ricci curvature; rigidity and compactness of Einstein metrics; general relativity; the stability of Minkowski space-time; and more.
Author | : Hubert Lewis Bray |
Publisher | : |
Total Pages | : 0 |
Release | : 2011 |
Genre | : General relativity (Physics). |
ISBN | : 9781571462305 |
Presents twenty-three selected survey articles on central topics of geometric analysis and general relativity, written by prominent experts in the fields. Topics of geometric analysis include the Yamabe problem, mean curvature flow, minimal surfaces, harmonic maps, collapsing of manifolds, and Kähler-Einstein metrics. General relativity topics include the positive mass theorem, the Penrose inequality, scalar curvature and Einstein's constraint equations, and the positive mass theorem for asymptotically hyperbolic manifolds.
Author | : Viktor Vasilʹevich Prasolov |
Publisher | : Cambridge University Press |
Total Pages | : 360 |
Release | : 2005-04-14 |
Genre | : Mathematics |
ISBN | : 0521547938 |
Topics covered range from computational complexity, algebraic geometry, dynamics, through to number theory and quantum groups.
Author | : Victor Guillemin |
Publisher | : American Mathematical Soc. |
Total Pages | : 500 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 0821816330 |
Symplectic geometry and the theory of Fourier integral operators are modern manifestations of themes that have occupied a central position in mathematical thought for the past three hundred years--the relations between the wave and the corpuscular theories of light. The purpose of this book is to develop these themes, and present some of the recent advances, using the language of differential geometry as a unifying influence.
Author | : Nicholas Young |
Publisher | : Cambridge University Press |
Total Pages | : 370 |
Release | : 2008 |
Genre | : Education |
ISBN | : 0521705649 |
A collection of articles showcasing the achievements of young Russian researchers in combinatorial and algebraic geometry and topology.
Author | : Silouanos Brazitikos |
Publisher | : American Mathematical Soc. |
Total Pages | : 618 |
Release | : 2014-04-24 |
Genre | : Mathematics |
ISBN | : 1470414562 |
The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lovász-Simonovits conjecture. This book provides a self-contained and up to date account of the progress that has been made in the last fifteen years.
Author | : R.K. Lazarsfeld |
Publisher | : Springer Science & Business Media |
Total Pages | : 414 |
Release | : 2004-08-24 |
Genre | : History |
ISBN | : 9783540225331 |
This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Volume I is more elementary than Volume II, and, for the most part, it can be read without access to Volume II.
Author | : Gijs J. O. Vermeer |
Publisher | : SEG Books |
Total Pages | : 369 |
Release | : 2012 |
Genre | : Science |
ISBN | : 1560803037 |
Details the properties of 3D acquisition geometries and shows how they naturally lead to the 3D symmetric sampling approach to 3D survey design. Many examples are used to illustrate choices of acquisition parameters, and the link between survey parameters and noise suppression as well as imaging is an intrinsic part of the contents.