Geometry

This research monograph provides a comprehensive study of a conjecture initially proposed by the second author at the 1998 International Congress of Mathematicians (ICM).

This book collects papers presented in the Invited Workshop, "e;Liutex and Third Generation of Vortex Definition and Identification for Turbulence,"e; from CHAOS2020, June 9-12, 2020, which was held online as a virtual conference.

This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments.

In the theory of minimal submanifolds, Bernstein's problem and Plateau's problem are central topics.

The focus of this monograph is converting-reshaping-one 3D convex polyhedron to another via an operation the authors call "e;tailoring.

This book consists of two parts.

This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions.

This book contains a systematic exposition of the theory of spinors in finite-dimensional Euclidean and Riemannian spaces.

The goal of this book is to investigate further the interdisciplinary interaction between Mathematical Analysis and Topology.

Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood.

Es gibt in der Differentialgeometrie von Kurven und FJachen zwei Betrachtungsweisen.

A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K.

The world''s leading authorities describe the state of the art in Serre''s conjecture and rational points on algebraic varieties.

This book provides a comprehensive algebraic treatment of hypergroups, as defined by F.

In this book, the author writes freely and often humorously about his life, beginning with his earliest childhood days.

Although the monograph Progress in Optimization I: Contributions from Aus- tralasia grew from the idea of publishing a proceedings of the Fourth Optimiza- tion Day, held in July 1997 at the Royal Melbourne Institute of Technology, the focus soon changed to a refereed volume in optimization.

Collecting together the lecture notes of the CIME Summer School held in Cetraro in July 2018, the aim of the book is to introduce a vast range of techniques which are useful in the investigation of complex manifolds.

These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic.

Stochastic geometry deals with models for random geometric structures.

Anomalies are ubiquitous features in quantum field theories.

In this monograph on twistor theory and its applications to harmonic map theory, a central theme is the interplay between the complex homogeneous geometry of flag manifolds and the real homogeneous geometry of symmetric spaces.

This work provides the first classification theory of matrix-valued symmetry breaking operators from principal series representations of a reductive group to those of its subgroup.

A complete, self-contained introduction to a powerful and resurging mathematical discipline Combinatorial Geometry presents and explains with complete proofs some of the most important results and methods of this relatively young mathematical discipline, started by Minkowski, Fejes T th, Rogers, and Erd's.

The conical approach provides a geometrical understanding of optimization and is a powerful research tool and useful problem-solving technique (for example, in decision support and real time control applications).

Part 1 of this popular graduate-level textbook focuses on mathematical methods involving complex analysis, determinants, and matrices, including updated and additional material covering conformal mapping.

This monograph strives to introduce a solid foundation on the usage of Grobner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K.

This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere.

Intrinsically noncommutative spaces today are considered from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics.

Radiolaria are a very diverse marine siliceous microplankton group that have existed at least snice the Cambrian to the recent.

This highly readable book aims to ease the many challenges of starting undergraduate research.

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

The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering.

The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564.

Geometry is a classical core part of mathematics which, with its birth, marked the beginning of the mathematical sciences.

Dirac operators play an important role in several domains of mathematics and physics, for example: index theory, elliptic pseudodifferential operators, electromagnetism, particle physics, and the representation theory of Lie groups.

This book collects and explains the many theorems concerning the existence of certificates of positivity for polynomials that are positive globally or on semialgebraic sets.

This graduate textbook provides an introduction to quantum gravity, when spacetime is two-dimensional.

This book evaluates and suggests potentially critical improvements to causal set theory, one of the best-motivated approaches to the outstanding problems of fundamental physics.

This book represents the first synthesis of the considerable body of new research into positive definite matrices.

Important lectures on differential topology by acclaimed mathematician John MilnorThese are notes from lectures that John Milnor delivered as a seminar on differential topology in 1963 at Princeton University.

A Fields medalist recounts his lifelong effort to uncover the geometric shape-the Calabi-Yau manifold-that may store the hidden dimensions of our universe.