Surveys in Geometry I

Surveys in Geometry I PDF

Author: Athanase Papadopoulos

Publisher: Springer Nature

Published: 2022-02-18

Total Pages: 469

ISBN-13: 3030866955

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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.

Surveys on Recent Developments in Algebraic Geometry

Surveys on Recent Developments in Algebraic Geometry PDF

Author: Izzet Coskun

Publisher: American Mathematical Soc.

Published: 2017-07-12

Total Pages: 370

ISBN-13: 1470435578

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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.

Lectures and Surveys on G2-Manifolds and Related Topics

Lectures and Surveys on G2-Manifolds and Related Topics PDF

Author: Spiro Karigiannis

Publisher: Springer Nature

Published: 2020-05-26

Total Pages: 392

ISBN-13: 1071605771

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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. It provides an accessible introduction to various aspects of the geometry of G2 manifolds, including the construction of examples, as well as the intimate relations with calibrated geometry, Yang-Mills gauge theory, and geometric flows. It also features the inclusion of a survey on the new topological and analytic invariants of G2 manifolds that have been recently discovered. The first half of the book, consisting of several introductory lectures, is aimed at experienced graduate students or early career researchers in geometry and topology who wish to familiarize themselves with this burgeoning field. The second half, consisting of numerous survey articles, is intended to be useful to both beginners and experts in the field.

Surveys in Geometric Analysis and Relativity

Surveys in Geometric Analysis and Relativity PDF

Author: Hubert Lewis Bray

Publisher:

Published: 2011

Total Pages: 0

ISBN-13: 9781571462305

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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.

Surveys in Contemporary Mathematics

Surveys in Contemporary Mathematics PDF

Author: Nicholas Young

Publisher: Cambridge University Press

Published: 2008

Total Pages: 370

ISBN-13: 0521705649

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A collection of articles showcasing the achievements of young Russian researchers in combinatorial and algebraic geometry and topology.

Surveys on Discrete and Computational Geometry

Surveys on Discrete and Computational Geometry PDF

Author: Jacob E. Goodman

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 568

ISBN-13: 0821842390

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This volume contains nineteen survey papers describing the state of current research in discrete and computational geometry as well as a set of open problems presented at the 2006 AMS-IMS-SIAM Summer Research Conference Discrete and Computational Geometry--Twenty Years Later, held in Snowbird, Utah, in June 2006. Topics surveyed include metric graph theory, lattice polytopes, the combinatorial complexity of unions of geometric objects, line and pseudoline arrangements, algorithmic semialgebraic geometry, persistent homology, unfolding polyhedra, pseudo-triangulations, nonlinear computational geometry, $k$-sets, and the computational complexity of convex bodies.

Surveys in Modern Mathematics

Surveys in Modern Mathematics PDF

Author: Viktor Vasilʹevich Prasolov

Publisher: Cambridge University Press

Published: 2005-04-14

Total Pages: 360

ISBN-13: 0521547938

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Topics covered range from computational complexity, algebraic geometry, dynamics, through to number theory and quantum groups.

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