Objectif In this project we wish to explore theoretical, as well as practical, aspects of solving equations in free groups. We will first consider a particular type of equation that occurs while solving the endomorphism problem in free groups. We say that the endom orphism problem is solvable for an element W in a group G if it can be decided effectively whether or not, given U in G, there is an endomorphism of G sending Wto U. We aim to display a polynomial-time algorithm that solves the endomorphism problem in free groups and also analyse the endomorphism problem from the perspective of generic-time complexity as developed by Schupp, Kapovich, Myasnikov and Shpilrain.Another goal of this project is the classification of equations in free groups in the following sense. We call a group G separable with respect to a class of equations if, for every equation in the class with no solution in G, there is a finite quotient of G in which the equation has no solution. We want to determine what classes of equations the free groups are separable with respect to. Champ scientifique natural sciencescomputer and information sciencescomputational sciencenatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatoricsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programme(s) FP6-MOBILITY - Human resources and Mobility in the specific programme for research, technological development and demonstration "Structuring the European Research Area" under the Sixth Framework Programme 2002-2006 Thème(s) MOBILITY-2.1 - Marie Curie Intra-European Fellowships (EIF) Appel à propositions FP6-2002-MOBILITY-5 Voir d’autres projets de cet appel Régime de financement EIF - Marie Curie actions-Intra-European Fellowships Coordinateur CENTRE DE RECERCA MATEMATICA Contribution de l’UE Aucune donnée Adresse BELLATERRA Espagne Voir sur la carte Liens Site web Opens in new window Coût total Aucune donnée
