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Topology, Geometry and Group Theory, Informed by Experiment (October 21-25, 2013)


Organizing Committee
  • Danny Calegari
    (Cambridge University)
  • Marc Culler
    (University of Illinois, Chicago)
  • David Gabai
    (Princeton University)
  • Joel Hass
    (UC Davis)
  • Robert Lipshitz
    (Columbia University)
  • Karen Vogtmann
    (Cornell University)
  • Genevieve Walsh
    (Tufts University)

 

Description

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.

  • Christoph Schwab *
    (ETH)
  • Aarti Singh*
    (Carnegie Mellon University)
  • Maxim Skriganov
    (Russian Academy of Sciences)
  • Ian Sloan *
    (University of New South Wales)
  • Gongguo Tang*
    (University of Wisconsin)
  • Vladimir Temlyakov
    (University of South Carolina)
  • Mike Wakin
    (Colorado School of Mines)
  • Grzegorz Wasilkowski
    (University of Kentucky)
  • Rebecca Willett
    (University of Wisconsin)
  • Przemyslaw Wojtaszczyk*
    (University of Warsaw)
  • Henryk Wozniakowski *
    (Columbia University)
  • John Wright*
    (Columbia University)
  • Ozgur Yilmaz
    (University of British Columbia)
  • Wotao Yin*
    (Rice University)
  • Xiaoqun Zhang
    (Shanghai Jiaotong University)
ThursdayOctober 17, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
10:30 - 11:50Topics in geometric structures Rich Schwartz, Brown University11th Floor Lecture Hall
1:30 - 3:00Hyperbolic 3-ManifoldsJeff Brock, Brown University11th Floor Lecture Hall
3:00 - 3:30Coffee Break11th Floor Collaborative Space
3:30 - 5:00Floer Theory Robert Lipshitz, Columbia University11th Floor Lecture Hall

FridayOctober 18, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
10:30 - 12:00Cube complexes & boundariesKim Ruane, Tufts University11th Floor Lecture Hall
1:30 - 3:00Surfaces & Mod_gJing Tao, University of Oklahoma11th Floor Lecture Hall
3:00 - 3:30Coffee Break11th Floor Collaborative Space
3:30 - 5:00Floer Theory Robert Lipshitz, Columbia University11th Floor Lecture Hall

MondayOctober 21, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
8:30 - 8:55Registration: Topology, Geometry and Group Theory, Informed by Experiment Workshop11th Floor Lecture Hall and Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:50Arithmetic and congruence linksAlan Reid, University of Texas at Austin11th Floor Lecture Hall
PDF
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:20A Parameter Space for Potential Small Cusped Hyperbolic 3-ManifoldsRobert Meyerhoff, Boston College11th Floor Lecture Hall
PDF
11:30 - 12:20Higher Differentials in Khovanov HomologyJoshua Batson, MIT11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch and Free Time
2:30 - 3:20Culler-Vogtmann's Outer space and the geometry of Out(F_n)Mark Feighn, Rutgers University11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:50Integer homology 3-spheres with large injectivity radiusNathan Dunfield, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
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5:00 - 6:30Welcome Reception 11th Floor Collaborative Space

TuesdayOctober 22, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:50Contracting BoundariesRuth Charney, Brandeis University11th Floor Lecture Hall
PDF
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:20A Khovanov stable homotopy type and new s-invariantsSucharit Sarkar, Princeton University11th Floor Lecture Hall
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11:30 - 12:20Surface maps into orbifoldsAlden Walker, University of Chicago11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch and Free Time
2:30 - 3:20Floer homology and Fractional Dehn twistsMatthew Hedden, Michigan State University11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:50Problems in 3-dimensional topologyIan Agol, University of California, Berkeley11th Floor Lecture Hall
PDF

WednesdayOctober 23, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:50Whitehead's algorithm, Heegaard splittings, and virtual geometricityJason Manning, University at Buffalo (SUNY)11th Floor Lecture Hall
PDF
10:00 - 10:30Coffee/ Tea Break11th Floor Collaborative Space
10:30 - 11:20Hyperbolic geometry of compression bodiesJessica Purcell, Brigham Young University11th Floor Lecture Hall
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11:30 - 12:20A new combinatorial class of triangulationsStephan Tillmann, University of Sydney11th Floor Lecture Hall
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12:30 - 12:40Group Photo11th Floor Lecture Hall
12:40 - 2:00Break for Lunch and Free Time
2:00 - 2:25SnapPy: computing hyperbolic structures on 3-manifoldsNathan Dunfield, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
2:30 - 2:55Twister: 3-Manifolds from Mapping ClassesMark Bell, University of Warwick11th Floor Lecture Hall
3:00 - 3:20Coffee/Tea Break11th Floor Collaborative Space
3:25 - 3:50ptolemy: PGL(n,C)-representations of 3-manifoldsMatthias Görner, University of Maryland11th Floor Lecture Hall
3:55 - 4:15Verified Computations in 3-manifoldsNeil Hoffman, University of Melbourne11th Floor Lecture Hall
4:20 - 4:35Scallop DemoAlden Walker, University of Chicago11th Floor Lecture Hall
4:40 - 5:05Regina: Triangulations, normal surfaces and other goodiesBen Burton, University of Queensland11th Floor Lecture Hall
5:10 - 5:203D printing mathematicsSaul Schleimer, University of Warwick11th Floor Lecture Hall
7:00 - 8:30Poster Session and Dessert Reception11th Floor Lecture Hall and Collaborative Space

ThursdayOctober 24, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:50Computations in Heegaard Floer homologyDylan Thurston, Indiana University11th Floor Lecture Hall
PDF
10:00 - 10:30Coffee/ Tea Break11th Floor Collaborative Space
10:30 - 11:20How (not) to compute a character variety (and get some insight anyway)Luisa Paoluzzi, Aix-Marseille University11th Floor Lecture Hall
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11:30 - 12:20An infinite rank summand of topologically slice knotsJennifer Hom, Columbia University11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch and Free Time
2:30 - 3:20The ptolemy module - a SnapPy tool to study PGL(N,C)-representations of 3-manifoldsMatthias Goerner, University of Maryland11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
3:30 - 3:30Survey DistributionSurvey will be emailed to you.
4:00 - 4:50The Malnormal Special Quotient TheoremDaniel Groves, University of Illinois11th Floor Lecture Hall
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FridayOctober 25, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:50Compressed words in Gromov hyperbolic groupsSaul Schleimer, University of Warwick11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:20The Big Dehn surgery graph and the link of S^3Genevieve Walsh, Tufts University11th Floor Lecture Hall
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11:30 - 12:20Computational surprises: mathematical programming and normal surface theoryBen Burton, University of Queensland11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch and Free Time
2:30 - 3:20Finding killer wordsNathaniel Thurston, Google Inc.11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:503-Manifolds EverywhereDanny Calegari, University of Chicago11th Floor Lecture Hall
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