Zlil Sela

Zlil Sela (2010)

Zlil Sela ( Hebrew צליל סלע; *  May 3, 1962 ) is an Israeli group theorist who deals with geometric group theory (hyperbolic groups, elementary theory of free groups) and model theory and their connections.

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

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

In the early 2000s he solved the Tarski problem (1945) by showing that two finitely generated non-Abelian 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), Olga Kharlampovich and Alexei Myasnikov published a proof in 2006, which Sela believes to be flawed.

In 2008 he received the Karp Prize for his work , especially for his solution to the isomorphism problem and the Tarski problem.

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

Web links

• Zlil Sela on the website of the Einstein Institute for Mathematics

References and comments

1. ↑ Zlil Sela in the Mathematics Genealogy Project (English)
2. ↑ It consists in showing when two representations belong to isomorphic groups. Sela in: Annals of Mathematics. Volume 141, 1995, p. 217.
3. ^ According to Mikhail Gromov
4. ^ Rips, Sela: Canonical representatives and equations in hyperbolic groups. In: Inventiones Mathematicae. Volume 120, 1995, pp. 489-512.
5. ↑ Sela: Diophantine Geometry over Groups. Part 1-6. In: Pub. Math. IHES. Volume 93, 2001, p. 31; Israel J. Math. Vol. 134, 2003, p. 173; Volume 143, 2004, p. 1; Volume 147, 2005, p. 1; Volume 150, 2005, p. 1; Geometry and Functional Analysis. Volume 16, 2006, pp. 537, 707.
6. ↑ Sela A report on Tarski's decidability problem. Preprint 2014.
7. ↑ Laudation ( Memento of the original from May 13, 2008 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.