This book provides an introduction to categorical Donaldson-Thomas (DT) theory, a rapidly developing field which has close links to enumerative geometry, birational geometry, geometric representation theory and classical moduli problems in algebraic geometry.
The history of describing natural objects using geometry is as old as the advent of science itself, in which traditional shapes are the basis of our intuitive understanding of geometry.
This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years.
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician.
DeMYSTiFieD is your solution for tricky subjects like trigonometryIf you think a Cartesian coordinate is something from science fiction or a hyperbolic tangent is an extreme exaggeration, you need Trigonometry DeMYSTiFieD, Second Edition, to unravel this topic's fundamental concepts and theories at your own pace.
This book presents a differential geometric method for designing nonlinear observers for multiple types of nonlinear systems, including single and multiple outputs, fully and partially observable systems, and regular and singular dynamical systems.
This book provides detailed information on index theories and their applications, especially Maslov-type index theories and their iteration theories for non-periodic solutions of Hamiltonian systems.
In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130].
This proceedings contains a collection of selected, peer-reviewed contributions from the 4th International Workshop "e;Differential Geometric Structures and Applications"e; held in Haifa, Israel from May 10-13, 2023.
Developing and providing an overview of recent results on nearly Kahler geometry on pseudo-Riemannian manifolds, this monograph emphasizes the differences with the classical Riemannian geometry setting.
Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of
This volume explores the interplay between mathematical and physical research and the interactions of twentieth-century scientists within their academic communities.
The book presents a general mathematical framework able to detect and to characterise, from a morphological and statistical perspective, patterns hidden in spatial data.
This book commemorates the 150th birthday of Corrado Segre, one of the founders of the Italian School of Algebraic Geometry and a crucial figure in the history of Algebraic Geometry.
Machine Intelligence and Pattern Recognition, Volume 2: Computational Geometry focuses on the operations, processes, methodologies, and approaches involved in computational geometry, including algorithms, polygons, convex hulls, and bucketing techniques.
This proceedings presents the latest research materials done on group theory from geometrical viewpoint in particular Gromov's theory of hyperbolic groups, Coxeter groups, Tits buildings and actions on real trees.
Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets.