François Dahmani : Algorithmic problems in groups with geometry of negative curvature: Dehn's isomorphism problem, and the equations problem.

Posted by Christian Rosendal , part of the Departmental Colloquium.

At

Nov. 11, 2011, 3 p.m.

In

SEO 636

Abstract

In the continuation of Hilbert's Xth problem on diophantine equations, Dehn proposed in 1912 three fundamental problems in (finitely generated) group theory; the word problem, the conjugacy problem and the isomorphism problem. The questions are to detect when two given elements of a given group are the same, are conjugate, and when two given groups are isomorphic. Although, as it was discovered in the 50's, these problems are algorithmically undecidable in general, in presence of geometry of negative curvature, one can usually solve the word problem and the conjugacy problem somewhat easily. The problems of equations, and of isomorphism are harder in many respects, but their study has highlighted some deep structures, and helped introduce powerful tools.