Effective and Algorithmic Methods in Hyperbolic Geometry and Free Groups
(May 16  20, 2016)
The recent proof of Thurston's virtual fibering conjecture brought together tools at the forefront of geometric group theory, dynamics, and hyperbolic geometry. We still lack, however, an effective or constructive understanding of threedimensional hyperbolic geometry, and more generally, 3manifold topology. For example, a closed hyperbolic 3manifold admits a finite cover which fibers over the circle, but can one construct such a cover from a presentation of the fundamental group? Can one implement an algorithm  perhaps with the help of preexisting software such as SnapPea  to obtain such a cover?
While much work remains, both computation and theory have progressed. Fast algorithms have been developed for running computations in the mapping class group and other finitely generated groups, as well as for recognizing certain types 3manifolds and knot and link complements up to homeomorphism. These have been supplemented by a new wave of constructive theorems which explicitly relate the algebra of the fundamental group of a hyperbolic 3manifold to its geometry, and to the geometry of various simplicial complexes, such as the curve complex. This ICERM workshop will focus on such advances, as well as on the development of new algorithms and extension of algorithmic techniques to the study of free groups. The workshop aims to bring together researchers from a broad range of related fields to work towards a more effective and quantitative understanding of 3manifold topology, geometric group theory, and hyperbolic geometry.
Organizing Committee
 Tarik Aougab
(Brown University)  Jeffrey Brock
(Brown University)  Mladen Bestvina
(University of Utah)  Eriko Hironaka
(Florida State University)  Johanna Mangahas
(University at Buffalo)

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