Departmental Colloquium
François Dahmani
University of Grenoble
Algorithmic problems in groups with geometry of negative curvature: Dehn's isomorphism problem, and the equations problem.
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.
Friday November 11, 2011 at 3:00 PM in SEO 636