Services aux conférences Mandl

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.

Résumé: This workshop, sponsored by AIM and the NSF, will be devoted to the outer automorphism group of the free group, Out(F); in particular, its geometry and its inherent asymmetry.

Résumé: This conference deal with recent developments in Lie theory and its interaction with geometry and algebra, i.e., Deformation quantization, Cohomology, projective geometry, Hopf algebra, Lie (super)algebras and their representations. The development of the new commutative non associative algebras known as ``Lie antialgebras.''