Lectures on Coarse Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Coarse Geometry write by John Roe. This book was released on 2003. Lectures on Coarse Geometry available in PDF, EPUB and Kindle. Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This book provides a general perspective on coarse structures. It discusses results on asymptotic dimension and uniform embeddings into Hilbert space.
A Course in Metric Geometry
A Course in Metric Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Course in Metric Geometry write by Dmitri Burago. This book was released on 2022-01-27. A Course in Metric Geometry available in PDF, EPUB and Kindle. “Metric geometry” is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Carathéodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with “easy-to-touch” mathematical objects using “easy-to-visualize” methods. The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of the exposition.
Lectures on Formal and Rigid Geometry
Lectures on Formal and Rigid Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Formal and Rigid Geometry write by Siegfried Bosch. This book was released on 2014-08-22. Lectures on Formal and Rigid Geometry available in PDF, EPUB and Kindle. The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".
Coarse Geometry of Topological Groups
Coarse Geometry of Topological Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Coarse Geometry of Topological Groups write by Christian Rosendal. This book was released on 2021-12-16. Coarse Geometry of Topological Groups available in PDF, EPUB and Kindle. Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.
Berkeley Lectures on P-adic Geometry
Berkeley Lectures on P-adic Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Berkeley Lectures on P-adic Geometry write by Peter Scholze. This book was released on 2020-05-26. Berkeley Lectures on P-adic Geometry available in PDF, EPUB and Kindle. Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field. This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.
