Organizing Committee
Abstract

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 three-dimensional hyperbolic geometry, and more generally, 3-manifold topology. For example, a closed hyperbolic 3-manifold 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 3-manifolds 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 3-manifold 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 3-manifold topology, geometric group theory, and hyperbolic geometry.

Confirmed Speakers & Participants

Workshop Schedule

Monday, May 16, 2016
TimeEventLocationMaterials
8:30 - 8:55Registration11th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:50Normalizers of lone axis automorphisms - Yael Algom-Kfir, University of Haifa11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20Fast Nielsen-Thurston Classification - Dan Margalit, Georgia Tech11th Floor Lecture Hall
11:30 - 12:20Random nilpotent groups - Moon Duchin, Tufts University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:20The Kakimizu complex of a 3-manifold need not be quasi-Euclidean - Jennifer Schultens, University of California at Davis11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50Computing with relative train tracks - Mark Feighn, Rutgers University11th Floor Lecture Hall
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, May 17, 2016
TimeEventLocationMaterials
9:00 - 9:50Geometrically similar 3-manifolds - David Futer, Temple University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break and Poster Session11th Floor Collaborative Space 
10:30 - 11:20Homological representations of mapping class groups. - Asaf Hadari, University of Hawaii at Manoa11th Floor Lecture Hall
11:30 - 12:20The capacity dimension of the space of ending laminations and the asymptotic dimension of the curve complex - Ken Bromberg, University of Utah11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:20Veering triangulations and fibered faces of 3--manifolds - Samuel Taylor, Yale University11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break and Poster Session11th Floor Collaborative Space 
4:00 - 4:50Efficient geodesics and an effective algorithm for distance in the complex of curves - Joan Birman, Columbia University11th Floor Lecture Hall
Wednesday, May 18, 2016
TimeEventLocationMaterials
9:00 - 9:50Arithmetic quotients of automorphism groups of RAAGs - Karen Vogtmann, Cornell University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20Dynamics and splittings of free-by-cyclic groups - Chris Leininger, University of Illinois at Urbana Champaign11th Floor Lecture Hall
11:30 - 12:20L2-torsion of free-by-cyclic groups - Matt Clay, University of Arkansas11th Floor Lecture Hall
12:30 - 12:40Group Photo in Lecture Hall11th Floor Lecture Hall 
12:40 - 2:30Break for Lunch / Free Time  
2:30 - 3:20Efficient and effective quasimorphisms - Jing Tao, University of Oklahoma11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50Effective geometry change under drilling and filling - Jessica Purcell, Monash University11th Floor Lecture Hall
Thursday, May 19, 2016
TimeEventLocationMaterials
9:00 - 9:50Bounds for the first eigenvalue of the Laplacian for hyperbolic manifolds fibering over the circle. - Juan Souto, Universite de Rennes 111th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20Effective methods for subgroup separability and lifting curves simply - Priyam Patel, Purdue University11th Floor Lecture Hall
11:30 - 12:20The Teichmüller space contains non-convex round balls. - Kasra Rafi, University of Toronto11th Floor Lecture Hall 
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:20Hyperbolicity in Outer space and free group extensions - Spencer Dowdall, University of Illinois at Urbana Champaign11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50Basis conjugating outer automorphisms of RAAGs - Matthew Day, University of Arkansas11th Floor Lecture Hall
Friday, May 20, 2016
TimeEventLocationMaterials
9:00 - 9:50Polynomial-time algorithms on surfaces - Richard Webb, University of Cambridge11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20Boundaries of Kleinian groups. - Genevieve Walsh, Tufts University11th Floor Lecture Hall
11:30 - 12:20On the geomety of the flip graph - Valentina Disarlo, Indiana University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 4:00Collaboration and Work Time  
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 

Lecture Videos