Réunion du GDR-CNRS 2105 Tresses et topologie de petite dimension/

Meeting of the GDR-CNRS 2105 Braids and low dimensional Topology

Problèmes algorithmiques liés aux tresses et à la topologie de petite dimension/

Algorithmic Problems related with Braids and low dimensional Topology

Ile de Berder, Golfe du Morbihan du 15 au 17 novembre 2006/

Berder Island, Morbihan Gulf, November 15-17, 2006

Orateurs principaux/ Main Speakers: Ivan Dynnikov, Juan Gonzalez-Meneses, Patrick Dehornoy

Comité scientifique/ Scientific Commitee: Christian Blanchet, Patrick Dehornoy, Luis Paris, Bert Wiest

Programme/Program

Inscrits/Registered

Cette rencontre se tiendra du 15 au 17 novembre sur l'île de Berder dans le golfe du Morbihan, à une quinzaine de kilomètres de Vannes./

This meeting will take place from November 15 to 17 in Berder Island near Vannes.

Trois mini-cours sont prévus de chacun trois heures. /Three mini-courses are planned:

• Ivan Dynnikov (Moscou): Decision problems in low-dimensional topology

• Juan Gonzales-Meneses (Sevilla): Conjugacy problems in braid groups and other Garside groups.
  Abstract: In this series of talks we will review the known solutions to the "conjugacy decision problem" and the "conjugacy search problem" in Garside groups, with a special focus on braid groups. In the case of braid groups, we will explain how the geometric classification of braids is a significant issue with regards to conjugacy problems, and we will present a project developed jointly with J. Birman and V. Gebhardt, to find a polynomial solution to both conjugacy problems in braid groups. We will explain the achievements in this direction, toghether with recent work by other authors, and the open questions that remain. We will also discuss which of the above results generalize to other Garside groups.

• Patrick Dehornoy (Caen): Algorithmic problems connected with handle reduction of braids.

  Abstract: Handle reduction of braids is a simple algorithm for comparing braids with respect to their standard ordering and solving the isotopy problem. Paradoxically, this algorithm, which is both quite simple and extremely efficient in practice --- hence potentially useful for cryptographic applications --- is not well understood and its exact complexity is still unknown.
  In these lectures, we shall briefly review the (many) solutions to the isotopy problem of braids, and then specifically turn to handle reduction. We shall present the only proof presently known for the termination of the algorithm, and, in connection with recent work on braid combinatorics, explain why that proof seems far from optimal.
  
  

Des exposés d'une heure de préférence en relation avec les thèmes de la conférence compléteront le programme. One hour talks mostly in relation with the themes of the conference will complete the program./

L'accueil au centre de Berder se fera le mardi soir 14 novembre. /

The reception at Berder will be opened in evening Tuesday November 14.

Les exposés se feront à partir de 9h le mercredi 15, et finiront le vendredi 17 pour midi. /

Talks will take place form 9h on wednesday 15 to noon friday 17.