Dipartimento di Scienze di Base e Applicate per l'Ingegneria

Aula 1B1 (pal. RM002)

Olga Kharlampovich (Graduate Center and Hunter College CUNY)

Model theory and algebraic geometry in free and hyperbolic groups and
group algebras.

Abstract:
We discuss the modern theory of equations in groups, algebraic geometry
and model theory in free and hyperbolic groups. The development of
algebraic geometry comes together with advances in the theory of fully
residually free (limit groups) and fully residually hyperbolic groups,
which are coordinate groups of irreducible algebraic varieties. We
describe finitely generated groups elementarily equivalent to a free
non-abelian group, and definable sets in a free group. The Diophantine
problem in free and hyperbolic groups is decidable. We also discuss the
contrasting results on the undecidability of equations in Group algebras
of free and limit groups over a field and results on definability of the
geometry of a group in the theory of its group algebra.