Rizos Sklinos

This talk lies on the intersection of geometric group theory
with model theory. An interaction between the two disciplines was
initiated mostly by the profound work of Z. Sela on Tarski's problem
about the equality of the first order theories of non-Abelian free groups.

A stable first-order theory is a first-order theory that supports a
sufficiently nice independence relation, called forking independence.
Examples include algebraic independence in algebraically closed fields
and linear independence in vector spaces. Sela completely changed the
picture of stable groups (i.e. groups definable in a stable theory) when
he proved that torsion-free hyperbolic groups have a stable first order
theory. The only known families of stable groups up till then were
Abelian groups and algebraic groups (over algebraically closed fields).

In a joint work with C. Perin we give a geometric interpretation of
forking independence in non-Abelian free groups. Curve complexes played
a fundamental role in our proof, and simple cases of how the proof works
will be presented in this talk. No prior knowledge of first order logic
will be assumed.