Organizing Committee
Abstract

The mathematical focus of this workshop will include all aspects of the topology and geometry of low-dimensional manifolds and geometric group theory. It has been understood for over a century that these subjects are tightly connected, but the connections have become even deeper as the subjects have matured. Recent advances have given dramatic evidence of this. The workshop aims to further extend the interplay between these subjects.

Algorithms have been an important and consistent feature of all of these mathematical areas from the beginning. This includes both questions about the existence of algorithms and the development of practical algorithms for computing natural invariants. More recently, computer experiments and rigorous computer-assisted proofs have had a significant impact. It is natural to expect experimental and computational methods to play an expanding role in the theory of low dimensional spaces. Additional goals of the workshop are to explore the development of new computational tools and implementations of new algorithms, and to provide opportunities for researchers to become more familiar with existing tools and how they can be applied in research.

Image for "Topology, Geometry and Group Theory, Informed by Experiment"

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, October 21, 2013
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration: Topology, Geometry and Group Theory, Informed by Experiment Workshop11th Floor Lecture Hall and Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:50am EDTArithmetic and congruence links - Alan Reid, University of Texas at Austin11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTA Parameter Space for Potential Small Cusped Hyperbolic 3-Manifolds - Robert Meyerhoff, Boston College11th Floor Lecture Hall
11:30 - 12:20pm EDTHigher Differentials in Khovanov Homology - Joshua Batson, MIT11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch and Free Time  
2:30 - 3:20pm EDTCuller-Vogtmann's Outer space and the geometry of Out(F_n) - Mark Feighn, Rutgers University11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm EDTInteger homology 3-spheres with large injectivity radius - Nathan Dunfield, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
5:00 - 6:30pm EDTWelcome Reception 11th Floor Collaborative Space 
Tuesday, October 22, 2013
TimeEventLocationMaterials
9:00 - 9:50am EDTContracting Boundaries - Ruth Charney, Brandeis University11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTA Khovanov stable homotopy type and new s-invariants - Sucharit Sarkar, Princeton University11th Floor Lecture Hall
11:30 - 12:20pm EDTSurface maps into orbifolds - Alden Walker, University of Chicago11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch and Free Time  
2:30 - 3:20pm EDTFloer homology and Fractional Dehn twists - Matthew Hedden, Michigan State University11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm EDTProblems in 3-dimensional topology - Ian Agol, University of California, Berkeley11th Floor Lecture Hall
Wednesday, October 23, 2013
TimeEventLocationMaterials
9:00 - 9:50am EDTWhitehead's algorithm, Heegaard splittings, and virtual geometricity - Jason Manning, University at Buffalo (SUNY)11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/ Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTHyperbolic geometry of compression bodies - Jessica Purcell, Brigham Young University11th Floor Lecture Hall
11:30 - 12:20pm EDTA new combinatorial class of triangulations - Stephan Tillmann, University of Sydney11th Floor Lecture Hall
12:30 - 12:40pm EDTGroup Photo11th Floor Lecture Hall 
12:40 - 2:00pm EDTBreak for Lunch and Free Time  
2:00 - 2:25pm EDTSnapPy: computing hyperbolic structures on 3-manifolds - Nathan Dunfield, University of Illinois at Urbana-Champaign11th Floor Lecture Hall 
2:30 - 2:55pm EDTTwister: 3-Manifolds from Mapping Classes - Mark Bell, University of Warwick11th Floor Lecture Hall 
3:00 - 3:20pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:25 - 3:50pm EDTptolemy: PGL(n,C)-representations of 3-manifolds - Matthias Görner, University of Maryland11th Floor Lecture Hall 
3:55 - 4:15pm EDTVerified Computations in 3-manifolds - Neil Hoffman, University of Melbourne11th Floor Lecture Hall 
4:20 - 4:35pm EDTScallop Demo - Alden Walker, University of Chicago11th Floor Lecture Hall 
4:40 - 5:05pm EDTRegina: Triangulations, normal surfaces and other goodies - Ben Burton, University of Queensland11th Floor Lecture Hall 
5:10 - 5:20pm EDT3D printing mathematics - Saul Schleimer, University of Warwick11th Floor Lecture Hall 
7:00 - 8:30pm EDTPoster Session and Dessert Reception11th Floor Lecture Hall and Collaborative Space 
Thursday, October 24, 2013
TimeEventLocationMaterials
9:00 - 9:50am EDTComputations in Heegaard Floer homology - Dylan Thurston, Indiana University11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/ Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTHow (not) to compute a character variety (and get some insight anyway) - Luisa Paoluzzi, Aix-Marseille University11th Floor Lecture Hall
11:30 - 12:20pm EDTAn infinite rank summand of topologically slice knots - Jennifer Hom, Columbia University11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch and Free Time  
2:30 - 3:20pm EDTThe ptolemy module - a SnapPy tool to study PGL(N,C)-representations of 3-manifolds - Matthias Goerner, University of Maryland11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:30 - 3:30pm EDTSurvey Distribution - Survey will be emailed to you.  
4:00 - 4:50pm EDTThe Malnormal Special Quotient Theorem - Daniel Groves, University of Illinois11th Floor Lecture Hall
Friday, October 25, 2013
TimeEventLocationMaterials
9:00 - 9:50am EDTCompressed words in Gromov hyperbolic groups - Saul Schleimer, University of Warwick11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTThe Big Dehn surgery graph and the link of S^3 - Genevieve Walsh, Tufts University11th Floor Lecture Hall
11:30 - 12:20pm EDTComputational surprises: mathematical programming and normal surface theory - Ben Burton, University of Queensland11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch and Free Time  
2:30 - 3:20pm EDTFinding killer words - Nathaniel Thurston, Google Inc.11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm EDT3-Manifolds Everywhere - Danny Calegari, University of Chicago11th Floor Lecture Hall

Tutorial Week Schedule

Thursday, October 17, 2013
TimeEventLocationMaterials
10:30 - 11:50am EDTTopics in geometric structures - Rich Schwartz, Brown University11th Floor Lecture Hall 
1:30 - 3:00pm EDTHyperbolic 3-Manifolds - Jeff Brock, Brown University11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee Break11th Floor Collaborative Space 
3:30 - 5:00pm EDTFloer Theory - Robert Lipshitz, Columbia University11th Floor Lecture Hall 
Friday, October 18, 2013
TimeEventLocationMaterials
10:30 - 12:00pm EDTCube complexes & boundaries - Kim Ruane, Tufts University11th Floor Lecture Hall 
1:30 - 3:00pm EDTSurfaces & Mod_g - Jing Tao, University of Oklahoma11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee Break11th Floor Collaborative Space 
3:30 - 5:00pm EDTFloer Theory - Robert Lipshitz, Columbia University11th Floor Lecture Hall 

Associated Semester Workshops

Low-dimensional Topology, Geometry, and Dynamics
Image for "Low-dimensional Topology, Geometry, and Dynamics"
Sep 9 - Dec 6, 2013
Semester Program
Exotic Geometric Structures
Image for "Exotic Geometric Structures"
Sep 15 - 20, 2013
Semester Workshop

Lecture Videos

Finding killer words

Nathaniel Thurston
Google Inc.
October 25, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

Computational surprises: mathematical programming and normal surface theory

Benjamin Burton
University of Queensland
October 25, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

The Big Dehn surgery graph and the link of S^3

Genevieve Walsh
Tufts University
October 25, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

Compressed words in Gromov hyperbolic groups

Saul Schleimer
University of Warwick
October 25, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

The Malnormal Special Quotient Theorem

Daniel Groves
University of Illinois
October 24, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

The ptolemy module - a SnapPy tool to study PGL(N,C)-representations of 3-manifolds

Matthias Görner
University of Maryland
October 24, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

An infinite rank summand of topologically slice knots

Jennifer Hom
Columbia University
October 24, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

How (not) to compute a character variety (and get some insight anyway)

Luisa Paoluzzi
Aix-Marseille University
October 24, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

Computations in Heegaard Floer homology

Dylan Thurston
Indiana University
October 24, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

A new combinatorial class of triangulations

Stephan Tillmann
University of Sydney
October 23, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

Hyperbolic geometry of compression bodies

Jessica Purcell
Monash University
October 23, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

Whitehead's algorithm, Heegaard splittings, and virtual geometricity

Jason Manning
University at Buffalo (SUNY)
October 23, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

Floer homology and Fractional Dehn twists

Matthew Hedden
Michigan State University
October 22, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

Surface maps into orbifolds

Alden Walker
University of Chicago
October 22, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

A Khovanov stable homotopy type and new s-invariants

Sucharit Sarkar
Princeton University
October 22, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

Contracting Boundaries

Ruth Charney
Brandeis University
October 22, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

Integer homology 3-spheres with large injectivity radius

Nathan Dunfield
University of Illinois, Urbana-Champaign
October 21, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

Culler-Vogtmann's Outer space and the geometry of Out(F n)

Mark Feighn
Rutgers University
October 21, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

A Parameter Space for Potential Small Cusped Hyperbolic 3-Manifolds

Robert Meyerhoff
Boston College
October 21, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract

Arithmetic and congruence links

Alan Reid
University of Texas at Austin
October 21, 2013
Topology, Geometry and Group Theory, Informed by Experiment
Play     Abstract