# Zlil Sela

Zlil Sela (Hebrew צליל סלע; May 3, 1962) is an Israeli group theorists, the terrain of geometric group theory ( hyperbolic groups, elementary theory of free groups) and model theory, and their links busy.

Sela received his doctorate in 1991 from the Hebrew University in Eliyahu Rips. He was an associate (as Sloan Fellow ) Professor at Columbia University. He is currently a professor at the Albert Einstein Institute of Mathematics at the Hebrew University. With his teacher Rips he solved in the 1990s, the isomorphism problem for torsion-free hyperbolic groups. He led with Rips the JSJ decomposition of these groups (via the fundamental group of a graph of the group), later extended to two finitely presented torsion-free groups.

With Rips he proved with the same techniques, the algorithmic solvability of a finite system of equations in torsion-free hyperbolic groups.

The early 2000s, he solved the problem Tarski (1945 ) by showing that two finitely generated nonabelian free groups have the same first order theory ( "elementary equivalent" in the sense of model theory). For the rest of the conjecture ( decidability of the theory ) published Olga and Alexei Myasnikov Kharlampovich 2006 proof that Sela but holds to be faulty

In 2008 he received for his work on the Karp - price, especially for his solution of the isomorphism problem and the Tarski problem.

In 2003 he received the Erdös Award of the Israeli Mathematical Society. In 2005 he gave the Tarski Lectures at Berkeley. 2002 he was invited speaker on the ICM in Beijing ( Diophantine geometry over groups and the elementary theory of free and hyperbolic groups).