Algebraic topology

The 2007 Abel Symposium took place at the University of Oslo in August 2007.

This book contains the most recent progress in data assimilation in meteorology, oceanography and hydrology including land surface.

Topology as a subject, in our opinion, plays a central role in university education.

Providing a new approach to assembly maps, this book develops the foundations of coarse homotopy using the language of infinity categories.

At the heart of the topology of global optimization lies Morse Theory: The study of the behaviour of lower level sets of functions as the level varies.

A comprehensive treatment of Floer homology, based on the Seiberg–Witten equations, first published in 2007.

This book contains a self-consistent treatment of Besov spaces for W*-dynamical systems, based on the Arveson spectrum and Fourier multipliers.

Electrical, communication, transportation, computer, and neural networks are special kinds of nets.

Compactness is related to a number of fundamental concepts of mathemat- ics.

This book is a comprehensive treatment of the theory of persistence modules over the real line.

This monograph presents theoretical methods involving the Hamilton-Jacobi-Bellman formalism in conjunction with set-valued techniques of nonlinear analysis to solve significant problems in dynamics and control.

This volume originated in the workshop held at Nagoya University, August 28-30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category SH form a set.

The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of Riemann-Roch-Grothendieck for proper submersions.

"e;Symplectic Geometric Algorithms for Hamiltonian Systems"e; will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc.

This book introduces the reader to the most important concepts and problems in the field of l2-invariants.

This textbook on combinatorial commutative algebra focuses on properties of monomial ideals in polynomial rings and their connections with other areas of mathematics such as combinatorics, electrical engineering, topology, geometry, and homological algebra.

For many years, algebraic topology rests on three legs: "e;ordinary"e; cohomology, K-theory, and cobordism.

Algebraic K-Theory has become an increasingly active area of research.

The body of work presented in this book comes from research carried out since 2017 as part of the international "e;Actualite de Rene Thom"e; project.

The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives.

This book is about new topological invariants of real- and angle-valued maps inspired by Morse-Novikov theory, a chapter of topology, which has recently raised interest outside of mathematics; for example, in data analysis, shape recognition, computer science and physics.

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This volume provides a unified and accessible account of recent developments regarding the real homotopy type of configuration spaces of manifolds.

This book contains a self-consistent treatment of Besov spaces for W*-dynamical systems, based on the Arveson spectrum and Fourier multipliers.

The main goal of the CIME Summer School on "e;Algebraic Cycles and Hodge Theory"e; has been to gather the most active mathematicians in this area to make the point on the present state of the art.

The study of Lefschetz properties for Artinian algebras was motivated by the Lefschetz theory for projective manifolds.

Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications.

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.

A fundamental object of study in group theory is the lower central series of groups.

The book offers a comprehensive introduction to Leavitt path algebras (LPAs) and graph C*-algebras.

This monograph on the homotopy theory of topologized diagrams of spaces and spectra gives an expert account of a subject at the foundation of motivic homotopy theory and the theory of topological modular forms in stable homotopy theory.

This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values.

The special session on Decision Economics (DECON) is a scientific forum held annually, which is focused on sharing ideas, projects, research results, models, and experiences associated with the complexity of behavioural decision processes and socio-economic phenomena.

The topic of this book sits at the interface of the theory of higher categories (in the guise of (infinity,1)-categories) and the theory of properads.

This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors.

Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid's Elements.

This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry.

Locally semialgebraic spaces serve as an appropriateframework for studying the topological properties ofvarieties and semialgebraic sets over a real closed field.

A collection of research papers, both new and expository, based on the interests of Professor J.

MATRIX is Australia's international, residential mathematical research institute.

A new foundation of Topology, summarized under the name Convenient Topology, is considered such that several deficiencies of topological and uniform spaces are remedied.

An Introduction to Homological Algebra discusses the origins of algebraic topology.

At last, a friendly introduction to modern homotopy theory after Joyal and Lurie, reaching advanced tools and starting from scratch.