Monday, June 12, 2017 - 15:00
Seminario di Geometria
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.