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.

Image for "Effective and Algorithmic Methods in Hyperbolic Geometry and Free Groups"

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, May 16, 2016
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:50am EDTNormalizers of lone axis automorphisms - Yael Algom-Kfir, University of Haifa11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTFast Nielsen-Thurston Classification - Dan Margalit, Georgia Tech11th Floor Lecture Hall
11:30 - 12:20pm EDTRandom nilpotent groups - Moon Duchin, Tufts University11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:20pm EDTThe Kakimizu complex of a 3-manifold need not be quasi-Euclidean - Jennifer Schultens, University of California at Davis11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm EDTComputing with relative train tracks - Mark Feighn, Rutgers University11th Floor Lecture Hall
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, May 17, 2016
TimeEventLocationMaterials
9:00 - 9:50am EDTGeometrically similar 3-manifolds - David Futer, Temple University11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break and Poster Session11th Floor Collaborative Space 
10:30 - 11:20am EDTHomological representations of mapping class groups. - Asaf Hadari, University of Hawaii at Manoa11th Floor Lecture Hall
11:30 - 12:20pm EDTThe 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 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:20pm EDTVeering triangulations and fibered faces of 3--manifolds - Samuel Taylor, Yale University11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break and Poster Session11th Floor Collaborative Space 
4:00 - 4:50pm EDTEfficient 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 - 9:50am EDTArithmetic quotients of automorphism groups of RAAGs - Karen Vogtmann, Cornell University11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTDynamics and splittings of free-by-cyclic groups - Chris Leininger, University of Illinois at Urbana Champaign11th Floor Lecture Hall
11:30 - 12:20pm EDTL2-torsion of free-by-cyclic groups - Matt Clay, University of Arkansas11th Floor Lecture Hall
12:30 - 12:40pm EDTGroup Photo in Lecture Hall11th Floor Lecture Hall 
12:40 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:20pm EDTEfficient and effective quasimorphisms - Jing Tao, University of Oklahoma11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm EDTEffective geometry change under drilling and filling - Jessica Purcell, Monash University11th Floor Lecture Hall
Thursday, May 19, 2016
TimeEventLocationMaterials
9:00 - 9:50am EDTBounds 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 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTEffective methods for subgroup separability and lifting curves simply - Priyam Patel, Purdue University11th Floor Lecture Hall
11:30 - 12:20pm EDTThe shape of the moduli space - Kasra Rafi, University of Toronto11th Floor Lecture Hall 
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:20pm EDTHyperbolicity in Outer space and free group extensions - Spencer Dowdall, University of Illinois at Urbana Champaign11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm EDTBasis conjugating outer automorphisms of RAAGs - Matthew Day, University of Arkansas11th Floor Lecture Hall
Friday, May 20, 2016
TimeEventLocationMaterials
9:00 - 9:50am EDTPolynomial-time algorithms on surfaces - Richard Webb, University of Cambridge11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTBoundaries of Kleinian groups. - Genevieve Walsh, Tufts University11th Floor Lecture Hall
11:30 - 12:20pm EDTOn the geomety of the flip graph - Valentina Disarlo, Indiana University11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 4:00pm EDTCollaboration and Work Time  
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 

Lecture Videos