The hexaflexagon is a folded paper strip of colored triangles that has long delighted people with how it "e;magically"e; changes its appearance when "e;flexed"e;.
The NATO Advanced Study Institute on "e;The Arithmetic and Geometry of Algebraic Cycles"e; was held at the Banff Centre for Conferences in Banff (Al- berta, Canada) from June 7 until June 19, 1998.
After some decades of work a satisfactory theory of quantum gravity is still not available; moreover, there are indications that the original field theoretical approach may be better suited than originally expected.
The articles in this volume are devoted to:- moduli of coherent sheaves;- principal bundles and sheaves and their moduli;- new insights into Geometric Invariant Theory;- stacks of shtukas and their compactifications;- algebraic cycles vs.
Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references.
The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in nonlin- ear analysis during the last three decades.
These are notes from a graduate student course on algebraic topology and K-theory given by Daniel Quillen at the Massachusetts Institute of Technology during 1979-1980.
Three-dimensional topology includes two vast domains: the study of geometric structures on 3-manifolds and the study of topological invariants of 3-manifolds, knots, etc.
Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references.
This book contains the results of work done during the years 1967-1970 on fixed-point-free involutions on manifolds, and is an enlarged version of the author's doctoral dissertation [54J written under the direction of Professor William Browder.
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.
A NATO Advanced Study Institute entitled "e;Algebraic K-theory: Connections with Geometry and Topology"e; was held at the Chateau Lake Louise, Lake Louise, Alberta, Canada from December 7 to December 11 of 1987.
The volume includes papers from the WSCMO conference in Braunschweig 2017 presenting research of all aspects of the optimal design of structures as well as multidisciplinary design optimization where the involved disciplines deal with the analysis of solids, fluids or other field problems.
This book focuses on the properties of nonlinear systems of PDE with geometrical origin and the natural description in the language of infinite-dimensional differential geometry.
This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications.
From the reviews of the 1st edition:"e;This book provides a comprehensive and detailed account of different topics in algorithmic 3-dimensional topology, culminating with the recognition procedure for Haken manifolds and including the up-to-date results in computer enumeration of 3-manifolds.
This book consists of five chapters presenting problems of current research in mathematics, with its history and development, current state, and possible future direction.
A Nash manifold denotes a real manifold furnished with algebraic structure, following a theorem of Nash that a compact differentiable manifold can be imbedded in a Euclidean space so that the image is precisely such a manifold.
