Geometry

In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume.

This interdisciplinary volume collects contributions from experts in their respective fields with as common theme diagrams.

The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays.

This textbook is a comprehensive and yet accessible introduction to non-Euclidean Laguerre geometry, for which there exists no previous systematic presentation in the literature.

This book consists of contributions from the participants of the Abel Symposium 2019 held in Alesund, Norway.

This textbook provides a thorough introduction to the differential geometry of parametrized curves and surfaces, along with a wealth of applications to specific architectural elements.

This book highlights a number of recent research advances in the field of symplectic and contact geometry and topology, and related areas in low-dimensional topology.

This monograph presents recent developments in comparison geometry and geometric analysis on Finsler manifolds.

This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry.

This book collects a series of important works on noncommutative harmonic analysis on homogeneous spaces and related topics.

Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology.

This book pioneers a nonlinear Fredholm theory in a general class of spaces called polyfolds.

This is the second volume of the Handbook of the Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research.

Can artificial intelligence learn mathematics?

This book summarizes recent inventions, provides guidelines and recommendations, and demonstrates many practical applications of homomorphic encryption.

This concise textbook gathers together key concepts and modern results on the theory of holomorphic foliations with singularities, offering a compelling vision on how the notion of foliation, usually linked to real functions and manifolds, can have an important role in the holomorphic world, as shown by modern results from mathematicians as H.

This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras.

This monograph systematically explores the theory of rational maps between spheres in complex Euclidean spaces and its connections to other areas of mathematics.

This book covers methods of Mathematical Morphology to model and simulate random sets and functions (scalar and multivariate).

This book provides an overview of the latest progress on rationality questions in algebraic geometry.

This graduate textbook presents an approach through toric geometry to the problem of estimating the isolated solutions (counted with appropriate multiplicity) of n polynomial equations in n variables over an algebraically closed field.

This textbook offers a rigorous presentation of mathematics before the advent of calculus.

This volume arose from a semester at CIRM-Luminy on "e;Thermodynamic Formalism: Applications to Probability, Geometry and Fractals"e; which brought together leading experts in the area to discuss topical problems and recent progress.

This book contains the contributions resulting from the 6th Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDEs, which was held in Cortona (Italy) during the week of May 20-24, 2019.

This monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry.

This text is an enhanced, English version of the Russian edition, published in early 2021 and is appropriate for an introductory course in geometric control theory.

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 volume originated in talks given in Cortona at the conference "e;Geometric aspects of harmonic analysis"e; held in honor of the 70th birthday of Fulvio Ricci.

This brief focuses on the structural properties of nonlinear time-delay systems.

This book consists of two parts.

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 is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry.

This book introduces the reader to important concepts in modern applied analysis, such as homogenization, gradient flows on metric spaces, geometric evolution, Gamma-convergence tools, applications of geometric measure theory, properties of interfacial energies, etc.

What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common?

This book collects original peer-reviewed contributions to the conferences organised by the international research network "e;Minimal surfaces: Integrable Systems and Visualization"e; financed by the Leverhulme Trust.

A series of three symposia took place on the topic of trace formulas, each with an accompanying proceedings volume.

This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples.

This book presents important contributions to modern theories concerning the distribution theory applied to convex analysis (convex functions, functions of lower semicontinuity, the subdifferential of a convex function).

This concise textbook introduces the reader to advanced mathematical aspects of general relativity, covering topics like Penrose diagrams, causality theory, singularity theorems, the Cauchy problem for the Einstein equations, the positive mass theorem, and the laws of black hole thermodynamics.

This volume introduces some recent developments in Arithmetic Geometry over local fields.

This book is an outgrowth of the conference "e;Regulators IV: An International Conference on Arithmetic L-functions and Differential Geometric Methods"e; that was held in Paris in May 2016.

This book presents, in a clear and structured way, the set function \mathcal{T} and how it evolved since its inception by Professor F.

This book presents four lectures on Rees rings and blow-ups, Koszul modules with applications to syzygies, Grobner bases and degenerations, and applications of Adams operations.

This volume presents lectures given at the Wisla 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisla, Poland, and was organized by the Baltic Institute of Mathematics.

The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory.

The goal of this book is to provide an introduction to algebraic geometry accessible to students.

This book reports on an original approach to problems of loci.

This textbook provides an essential introduction to Lie groups, presenting the theory from its fundamental principles.

The theory presented in this work merges many concepts from mathematical optimization and real algebraic geometry.

This book presents a broad overview of the important recent progress which led to the emergence of new ideas in Lipschitz geometry and singularities, and started to build bridges to several major areas of singularity theory.