Geometric and Asymptotic Group Theory with Applications Geometric and Asymptotic Group Theory with Applications AMS Subject Classification: 20-XX A. Martino, V. Shpilrain i E. Ventura (editors) Escola Polit`ecnica Superior d’Enginyeria de Manresa ISBN-13: 978-84-86784-06-5 ISBN-10: 84-86784-06-9 Disseny de portada: Estudi Mestres Composici´oen LATEX: A. Roig Impressi´o:Remsa S.L. Manresa Manresa, 31 de juliol de 2006 Geometric and Asymptotic Group Theory with Applications Manresa (Catalunya) August 31st to September 4th, 2006 Organising committee: E. Ventura (coordinator) (Universitat Polit`ecnica de Catalunya), V. Shpilrain (City College of New York), A. Martino (Universitat Polit`ecnica de Catalunya), M. Sapir (Vanderbilt University), R. Gilman (Stevens Institute), J. Gonz´alez-Meneses (Universidad de Sevilla). Scientific committee: E. Ventura (Universitat Polit`ecnica de Catalunya), V. Shpilrain (City College of New York), A. Miasnikov (McGill Univerity), E. Zelmanov (University of California), C. Mart´ınez (Universidad de Oviedo), J. Burillo (Universitat Polit`ecnica de Catalunya), J. Villar (Universitat Polit`ecnica de Catalunya). Local committee: M. Alsina (Universitat Polit`ecnica de Catalunya), R. Caparr´os(Universitat Polit`ecnica de Catalunya), A. Roig (Universitat Polit`ecnica de Catalunya). With the support of Oficina de Suport a la Recerca Matem`atica Societat Catalana de Matem`atiques 1 Foreword Wellcome everybody to the GAGTA conference, “Geometric and Asymptotic Group Theory with Applications”, held in Manresa (Catalonia) from August 31st to Septem- ber 4th, 2006. This meeting is one of the 64 satellite activities of the International Congress of Mathematicians, ICM2006, that has been recently held in Madrid. On the occasion of the ICM2006 and after the success of the “Barcelona Group Theory Conference” held in July 2005 at the “Centre de Recerca Matem`atica”, we thought it would be a good opportunity to organize an international conference on Geometric Group Theory, for the second time in Catalonia and in Spain. The organization of this second event shows good international connections of the catalan mathematical community in general and the vitality of Catalonia in this area of mathematics in particular, where the number and quality of Catalan researchers has been significantly growing in the last years. Our main goal in organizing GAGTA has been to offer another opportunity to the international comunity of researchers in Group Theory to meet and discuss recent developments in this interesting and important area of Mathematics. GAGTA is devoted to the study of a variety of topics in Geometric and Combinatorial Group Theory, including asymptotic and probabilistic methods, as well as algorithmic and computational topics related to groups. In addition, highlighting the very recent developments regarding “Group-based Cryptography” and emphasizing this interesting field of applications of Group Theory, one day of the conference will be specifically devoted to this subject: September 4th will be the “Cryptography Day”. Our first words of gratitude are to the University campus holding the conference: the EPSEM, the “Escola Polit`ecnica Superior d’Enginyeria de Manresa”. Both the Direction and the Administration of the EPSEM welcomed this conference with great enthusiasm and helped with a lot of details regarding local arrangements. Manresa is a middle size city located at the geographical center of Catalonia. It is also located at the very base of Montserrat mountains, the cultural and sentimental heart of Catalonia, too. The proximity to the big city of Barcelona (big in many senses) sometimes eclipses the visibility of the activities promoted and developed in the surrounding smaller cities. Holding GAGTA here on the Manresa University campus is a solid proof of the capability of Manresa and its institutions to hold academic events at the highest international level. In this sense, also non-academic institutions of the city have responded very well to the possibility of running GAGTA here. We 2 warmly thank the “Ajuntament de Manresa” (the City Hall) and the “Caixa Manresa” financial institution for their valuable support as sponsors of the conference, both at the financial and organizational levels. In summary, we are very grateful to the city of Manresa for its warm hospitality towards GAGTA, one of the first international research conferences in any field ever taken place here. We also wish to acknowledge, with thanks, the support received from other sponsors. Apart from the local ones mentioned in the previous paragraph, we have received a generous support from the following institutions. The “Departament de Matem`atica Aplicada III” (MA3), the host department of the main organizer, and the “Universitat Polit`ecnica de Catalunya” (UPC) as the general holding institution, both collabo- rating at the formal, financial, and practical levels; and the “Oficina de Suport a la Recerca Matem`atica” (OSRM) of the UPC offering valuable technical and human support. Also, our thanks go to the “Societat Catalana de Matem`atiques” (SCM), for its significant help in the framework of giving support to all the events related to Mathematics and held in (or organized from) Catalonia. Three governments provided generous financial support to the organization of GAGTA through their own promotion programmes for research activities. The “Generalitat de Catalunya”, the Catalan Government, following an established scientific policy even though not always having the appropriate recognition and budget from the Spanish Government; the “Ministerio de Educaci´ony Ciencia” of the Spanish Government; and the National Science Foundation of the USA, providing a generous support for American participants. All the sponsors have contributed at different levels, and from the organizing com- mittee we want to sincerely thank all of them with the same gratitude. Without any of these contributions the organization would be much more difficult; without all of them, altogether impossible. In this booklet you will find the detailed program of the conference, together with the list of speakers, and the titles and abstracts of their talks. In the program, you will also find social activities, including a dinner and a couple of promising cultural visits to Montserrat and Sant Benet, where we hope you can taste and touch a bit of the very rich history, tradition and culture of this country, Catalonia. We hope you will enjoy your stay in Manresa, wishing it to be very productive from the scientific point of view, and very pleasant at the same time. Enric Ventura On behalf of the GAGTA Organizing Committee. Program 4 Program Thursday, August 31st (Main Room) 8:30 - 9:30 Registration 9:30 - 10:00 Opening session Josep Burillo 10:00 - 11:00 “Orderings in braided Thompson’s Groups” (p. 14) 11:00 - 11:30 Coffee break Martin Lustig 11:30 - 12:30 “R-trees – currents – laminations: a delicate relationship” (p. 19) Gilbert Levitt 12:30 - 13:00 “Growth rates for automorphisms of free groups” (p. 19) Armando Martino 13:00 - 13:30 “Putting a metric on Outer Space” (p. 20) Sean Cleary 15:30 - 16:00 “Metric properties of braided Thompson’s groups” (p. 15) Sarah Rees 16:00 - 16:30 “Group geodesics: regularity, star-freedom and local testability” (p. 22) 16:30 - 17:00 Coffee break Tim Riley 17:00 - 17:30 “Diameter versus filling length in metric discs and in groups” (p. 24) Kanta Gupta 17:30 - 18:00 “Tree extensions of symmetric groups and automorphisms” (p. 17) 19:00 - 20:00 Reception at Manresa City Hall Program 5 Friday, September 1st (Main Room) Mark Sapir 9:00 - 10:00 “TBA” (p. 24) Paul Schupp 10:00 - 11:00 “Mostow-type rigidity as a property of randomness” (p. 25) 11:00 - 11:30 Photo + Coffee break Vladimir Shpilrain 11:30 - 12:00 “The word problem: new challenges” (p. 25) Patrick Dehornoy 12:00 - 12:30 “Algorithms for Garside groups” (p. 16) Luis Paris 12:30 - 13:00 “Direct decompositions of Coxeter groups” (p. 22) Anton Klyachko 13:00 - 13:30 “One-relator relative presentations” (p. 19) Trip to Montserrat 16:00 - 22:30 Concert 6 Program Saturday, September 2nd (Main Room) Oleg Bogopolski 9:00 - 10:00 “On a Magnus property for some one-relator groups” (p. 13) Brian Bowditch 10:00 - 11:00 “The classification of Kleinian groups” (p. 14) 11:00 - 11:30 Coffee break Alain Valette 11:30 - 12:00 “Proper isometric actions on Banach spaces” (p. 26) Gerhard Rosenberger 12:00 - 12:30 “On the surface group conjecture” (p. 24) Luis Ribes 12:30 - 13:00 “On quasifree profinite groups” (p. 23) Denis Osin 13:00 - 13:30 “Large groups and their periodic quotients” (p. 21) Contributed talks (Main Room, Room S1, Room S2) MR Fran¸cois Dahmani, “The isomorphism problem for some relatively hyperbolic groups” (p. 31). S1 Elena Bunina, “Elementary equivalence of Chevalley 15:20 - 15:40 groups” (p. 31). S2 Luda Markus-Epstein, “Reading Kurosh decomposition via subgroup graphs” (p. 35). MR Fran¸cois Gautero, “Combination theorem for relatively hyperbolic groups” (p. 33). 15:40 - 16:00 S1 Marius Buliga, “Dilatation structures” (p. 31). S2 Ki Hyoung Ko, “Weighted decompositions of generic braids” (p. 34). Program 7 MR Claas Roever, “TBA” (p. 36). S1 Alexey Muranov, “Finitely generated infinite simple 16:00 - 16:20 groups of infinite commutator width” (p. 35). S2 Daniele Otera, “Some refinements of the (simple) con- nectivity at infinity” (p. 36). MR Ashot Minasyan, “The SQ-universality and residual prop- erties of relatively hyperbolic groups” (p. 35). S1 Ahmad Erfanian, “Probability of generating simple groups 16:20 - 16:40 PSp(2m,q)” (p. 32). S2 Koji Fujiwara, “Asymptotic dimension of curve graphs” (p. 32). 16:40 - 17:00 Coffee break MR Donghi Lee, “An algorithm that decides translation equiv- alence” (p. 34). S1 Francesco Russo, “Groups with soluble minimax classes 17:00 - 17:20 of conjugate subgroups” (p. 36). S2 Vladimir Kisil, “Elliptic, parabolic and hyperbolic invari- ants of cycles” (p.