Morse Theoretic Methods In Nonlinear Analysis And In Symplectic Topology
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Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology
Author: Paul Biran
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-02-12
The papers collected in this volume are contributions to the 43rd session of the Seminaire ́ de mathematiques ́ superieures ́ (SMS) on “Morse Theoretic Methods in Nonlinear Analysis and Symplectic Topology.” This session took place at the Universite ́ de Montreal ́ in July 2004 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together young researchers from various parts of the world and to present to them some of the most signi cant recent advances in these areas. More than 77 mathematicians from 17 countries followed the 12 series of lectures and participated in the lively exchange of ideas. The lectures covered an ample spectrum of subjects which are re ected in the present volume: Morse theory and related techniques in in nite dim- sional spaces, Floer theory and its recent extensions and generalizations, Morse and Floer theory in relation to string topology, generating functions, structure of the group of Hamiltonian di?eomorphisms and related dynamical problems, applications to robotics and many others. We thank all our main speakers for their stimulating lectures and all p- ticipants for creating a friendly atmosphere during the meeting. We also thank Ms. Diane Belanger ́ , our administrative assistant, for her help with the organi- tion and Mr. Andre ́ Montpetit, our technical editor, for his help in the preparation of the volume.
Topological Complexity and Related Topics
Author: Mark Grant
language: en
Publisher: American Mathematical Soc.
Release Date: 2018-02-14
This volume contains the proceedings of the mini-workshop on Topological Complexity and Related Topics, held from February 28–March 5, 2016, at the Mathematisches Forschungsinstitut Oberwolfach. Topological complexity is a numerical homotopy invariant, defined by Farber in the early twenty-first century as part of a topological approach to the motion planning problem in robotics. It continues to be the subject of intensive research by homotopy theorists, partly due to its potential applicability, and partly due to its close relationship to more classical invariants, such as the Lusternik–Schnirelmann category and the Schwarz genus. This volume contains survey articles and original research papers on topological complexity and its many generalizations and variants, to give a snapshot of contemporary research on this exciting topic at the interface of pure mathematics and engineering.
Topology and Robotics
Author: Michael Farber
language: en
Publisher: American Mathematical Soc.
Release Date: 2007
Ever since the literary works of Capek and Asimov, mankind has been fascinated by the idea of robots. Modern research in robotics reveals that along with many other branches of mathematics, topology has a fundamental role to play in making these grand ideas a reality. This volume summarizes recent progress in the field of topological robotics--a new discipline at the crossroads of topology, engineering and computer science. Currently, topological robotics is developing in two main directions. On one hand, it studies pure topological problems inspired by robotics and engineering. On the other hand, it uses topological ideas, topological language, topological philosophy, and specially developed tools of algebraic topology to solve problems of engineering and computer science. Examples of research in both these directions are given by articles in this volume, which is designed to be a mixture of various interesting topics of pure mathematics and practical engineering.