Kategoria BISAC: Mathematics >> Algebra - Abstract

The Festschrift in celebration of John William Helton's pioneering work, Mathematical Methods in Systems, Optimization, and Control comprises a careful selection of articles on systems and control theory, operator theory, and optimization. The book follows Helton's original and long lasting contributions which have shaped control theory and operator theory during the last decades, with specific emphasis on topics aimed at direct applications to current research areas of high impact and interest.

The book, by virtue of its diverse contents, strong interdisciplinary contents,...

Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. This has been the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central theme of his subsequent mathematical work. Tamari lattices can be realized in terms of polytopes called associahedra, which in fact also appeared first in Tamari's thesis.

By now these beautiful structures have made their appearance in many different areas of pure and applied mathematics, such as algebra, combinatorics, computer science, category theory, geometry, topology, and also in...

The 2007 Abel Symposium took place at the University of Oslo in August 2007. The goal of the symposium was to bring together mathematicians whose research efforts have led to recent advances in algebraic geometry, algebraic K-theory, algebraic topology, and mathematical physics. A common theme of this symposium was the development of new perspectives and new constructions with a categorical flavor. As the lectures at the symposium and the papers of this volume demonstrate, these perspectives and constructions have enabled a broadening of vistas, a synergy between once-differentiated...

Coalgebraic logic is an important research topic in the areas of concurrency theory, semantics, transition systems and modal logics. It provides a general approach to modeling systems, allowing us to apply important results from coalgebras, universal algebra and category theory in novel ways. Stochastic systems provide important tools for systems modeling, and recent work shows that categorical reasoning may lead to new insights, previously not available in a purely probabilistic setting.

This book combines coalgebraic reasoning, stochastic systems and logics. It provides an insight...

Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. They also touch on some aspects of topology, geometry and number theory. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focuses specifically on the ring theoretic properties of polycyclic groups and their applications, often to purely group theoretic situations.

In many areas of mathematics some higher operations are arising. These havebecome so important that several research projects refer to such expressions. Higher operationsform new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to...

The Abel Symposium 2009 "Combinatorial aspects of Commutative Algebra and Algebraic Geometry," held at Voss, Norway, featured talks by leading researchers in the field.

This is the proceedings of the Symposium, presenting contributions on syzygies, tropical geometry, Boij-Soderberg theory, Schubert calculus, and quiver varieties. The volume also includes an introductory survey on binomial ideals with applications to hypergeometric series, combinatorial games and chemical reactions.

The contributions pose interesting problems, and offer up-to-date research on...

The Bialowieża workshops on Geometric Methods in Physics are among the most important meetings in the field. Every year some 80 to 100 participants from both mathematics and physics join to discuss new developments and to interchange ideas. This volume contains contributions by selected speakers at the XXX meeting in 2011 as well as additional review articles and shows that the workshop remains at the cutting edge of ongoing research.

The 2011 workshop focussed on the works of the late Felix A. Berezin (1931-1980) on the occasion of his 80th anniversary as well as on Bogdan...

In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and a topic of research to this day. Arising from notes for a course given at the University of Bonn in Germany, "Plane Algebraic Curves" reflects the authorsʼ concern for the student audience through its emphasis on motivation, development of imagination, and understanding of basic ideas. As classical objects, curves may be viewed from many angles. This...