Effective and Algorithmic Methods in Hyperbolic Geometry and Free Groups
(May 16 - 20, 2016)

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Description

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.


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)

= speaker   = poster presenter

Monday May 16, 2016
Time Description Speaker Location Abstracts Slides
8:30 - 8:55Registration11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:50Normalizers of lone axis automorphismsYael Algom-Kfir, University of Haifa11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:20Fast Nielsen-Thurston ClassificationDan Margalit, Georgia Tech11th Floor Lecture Hall
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11:30 - 12:20Random nilpotent groupsMoon Duchin, Tufts University11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch / Free Time
2:30 - 3:20The Kakimizu complex of a 3-manifold need not be quasi-EuclideanJennifer Schultens, University of California at Davis11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:50Computing with relative train tracksMark Feighn, Rutgers University11th Floor Lecture Hall
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5:00 - 6:30Welcome Reception11th Floor Collaborative Space

Tuesday May 17, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:50Geometrically similar 3-manifoldsDavid Futer, Temple University11th Floor Lecture Hall
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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
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11:30 - 12:20The capacity dimension of the space of ending laminations and the asymptotic dimension of the curve complexKen Bromberg, University of Utah11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch / Free Time
2:30 - 3:20Veering triangulations and fibered faces of 3--manifoldsSamuel Taylor, Yale University11th Floor Lecture Hall
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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 curvesJoan Birman, Columbia University11th Floor Lecture Hall
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Wednesday May 18, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:50Arithmetic quotients of automorphism groups of RAAGsKaren Vogtmann, Cornell University11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:20Dynamics and splittings of free-by-cyclic groupsChris Leininger, University of Illinois at Urbana Champaign11th Floor Lecture Hall
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11:30 - 12:20L2-torsion of free-by-cyclic groupsMatt Clay, University of Arkansas11th Floor Lecture Hall
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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 quasimorphismsJing Tao, University of Oklahoma11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:50Effective geometry change under drilling and fillingJessica Purcell, Monash University11th Floor Lecture Hall
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Thursday May 19, 2016
Time Description Speaker Location Abstracts Slides
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
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:20Effective methods for subgroup separability and lifting curves simplyPriyam Patel, Purdue University11th Floor Lecture Hall
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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 extensionsSpencer Dowdall, University of Illinois at Urbana Champaign11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:50Basis conjugating outer automorphisms of RAAGsMatthew Day, University of Arkansas11th Floor Lecture Hall
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Friday May 20, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:50Polynomial-time algorithms on surfacesRichard Webb, University of Cambridge11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:20Boundaries of Kleinian groups.Genevieve Walsh, Tufts University11th Floor Lecture Hall
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11:30 - 12:20On the geomety of the flip graphValentina Disarlo, Indiana University11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch / Free Time
2:30 - 4:00Collaboration and Work Time
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space