Services aux conférences Mandl

Résumé: For years, computers have also played a key role in investigating the most central questions in the analytic theory of automorphic forms such as the existence of Maass wave forms. Recently, a team of researchers, including M. Rubinstein (Waterloo) and W. Stein (Seattle), has embarked on an ambitious collaborative effort to systematically gather vast amounts of data concerning, among other things, automorphic forms on higher rank groups. This effort is part of a three year (2008-2011) NSF funded Focused Research Group (FRG) grant dealing with L-functions and automorphic forms. The FRG effort is sure to generate challenges and new questions for people working both on the theoretical and the experimental side of the subject, as well as gathering valuable data that will be precious in suggesting conjectures or revealing new lines of enquiry.

Résumé: This workshop will be devoted to the study of a variety of topics in geometric and asymptotic group theory, with special emphasis on statistical methods and their applications (in theoretical cryptography). We have contributed to the organization of three similar conferences: in Manresa (Spain) in 2006, in Dortmund (Germany) in 2007, in New York in March 2008. We plan to gather leading specialists in various aspects of geometric, asymptotic, and algorithmic group theory. More specifically, the workshop topics will include quasi-isometries, isoperimetric functions, function growth, asymptotic invariants, random walks, algorithmic problems, etc.

Résumé: During the past 20 years, geometric group theory has developed many different facets, including relations with geometry, topology, analysis, and logic. The new, more geometric, perspectives have enabled rapid progress on many of these fronts. A tremendous solidification of previously disparate results has also occurred. In algorithmic group theory, in recent years, more and more interconnections between computer science and classical group and semigroup theory have been discovered. Automata theory has motivated the definition of new classes of groups, for instance, automaton groups and automatic groups. Techniques from rewriting theory, data compression, and automata theory are used in order to solve more efficiently word problems as well as other computational problems in (semi)group theory. The program of the workshop will capitalize on this recent surge of activity in both areas.

Résumé: In his seminal book 'Trees', Serre laid down the fundamentals of the theory of groups acting freely on simplicial trees. In the following decade Serre's novel approach unified several geometric, algebraic, and combinatorial methods of group theory into a unique powerful tool, known today as Bass-Serre Theory. Topologists became interested in R-trees with the work of Morgan and Shalen (1985) which generalized parts of Thurston's Geometrization Theorem. A joint effort of several researchers culminated in a description of finitely generated groups acting freely on R-trees, which is now known as Rips' theorem. The key ingredient of the theory is the so-called 'Rips machine'. The idea of the Rips machine comes from Makanin's algorithm (or elimination process) for solving equations in free groups.

Résumé: Solving equations is one of the main topics in mathematics. A more general and more difficult problem is to describe which formulas of the first-order logic hold in a given group. Recent works on the Tarski's problems (Kharlampovich, Miasnikov, Sela) opened a new direction of research called now 'Algebraic geometry over groups'. We are going to discuss some methods and techniques used for the solution of these problems, and developments in the algebraic geometry for groups, Lie Algebras, and other algebraic systems.