Organizing Committee
Abstract

This workshop will focus on recent advances in combinatorial link homology theories (e.g., Heegaard-Floer homology and Khovanov homology), especially as they apply to questions about braids and, more generally, mapping class groups of surfaces. There will be short mini-courses on

  1. Combinatorial knot Floer homology, with applications to contact geometry,
  2. Braid foliations and the Jones conjecture,
  3. Nielsen-Thurston theory, and
  4. Garside theory and a linear order on the braid group,
along with a number of research and expository talks. The talks will emphasize the role that computation and experiment have thus far played in stating key conjectures and establishing key results. The workshop will culminate in a computational problem session, in which participants will discuss promising directions for future exploration and indicate which computations may be most useful in that exploration.

As the main goal of the workshop is to facilitate interaction across a broad swath of the low-dimensional topology community, all talks will be at a level appropriate for "non-experts." Graduate students and early career researchers interested in learning the big open problems in this area--as well as the main techniques at hand to approach them--are particularly encouraged to apply.

This workshop is partially funded by NSF CAREER award DMS-1151671.

Image for "Combinatorial Link Homology Theories, Braids, and Contact Geometry"
Image Courtesy: John Baldwin

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, August 4, 2014
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 10:30am EDTMinicourse- Braid Foliations I - Doug LaFountain, Western Illinois University11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00pm EDTComputational complexity of problems in 3-dimensional topology - Nathan Dunfield, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
12:00 - 2:00pm EDTBreak for Lunch  
2:00 - 3:30pm EDTMinicourse- Nielsen-Thurston theory I - Johanna Mangahas, Brown University11th Floor Lecture Hall 
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 5:00pm EDTFoliations, Flows, and Contact Structures - Rachel Roberts, Washington University11th Floor Lecture Hall
5:15 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, August 5, 2014
TimeEventLocationMaterials
9:00 - 10:30am EDTMinicourse- Braid Foliations II - Doug LaFountain, Western Illinois University11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00pm EDTIntro. to Legendrian & Transverse Knots - John Etnyre, Georgia Institute of Technology11th Floor Lecture Hall 
12:00 - 2:00pm EDTBreak for Lunch  
2:00 - 3:30pm EDTMinicourse- Nielsen-Thurston theory II - Joanna Mangahas, Brown University11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 5:00pm EDTTeichmueller polynomials for free-by-cyclic groups and clique polynomials of digraphs - Eriko Hironaka, Florida State University11th Floor Lecture Hall
Wednesday, August 6, 2014
TimeEventLocationMaterials
9:00 - 10:30am EDTMinicourse- Grid Diagrams and Contact Geometry I - Lenhard Ng, Duke University11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00pm EDTRectangular Diagrams and Jones' Conjecture I- monotonic simplification and Legendrian links - Ivan Dynnikov, Moscow State University11th Floor Lecture Hall
12:10 - 12:20pm EDTGroup Photo11th Floor Lecture Hall 
12:20 - 2:00pm EDTBreak for Lunch  
2:00 - 3:00pm EDTRectangular Diagrams and Jones' Conjecture II- Legendrian graphs, bypasses and simplifying disks - Maxim Prasolov, Moscow State University11th Floor Lecture Hall
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:30 - 5:00pm EDTMinicourse- Garside structure and Dehornoy ordering of braid groups for topologists I - Tetsuya Ito, Kyoto University11th Floor Lecture Hall
Thursday, August 7, 2014
TimeEventLocationMaterials
9:00 - 10:30am EDTMinicourse- Grid Diagrams and Contact Geometry II - Lenhard Ng, Duke University11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00pm EDTDivide knots vs L-space knots - Ken Baker, University of Miami11th Floor Lecture Hall
12:00 - 2:00pm EDTBreak for Lunch  
2:00 - 3:30pm EDTMinicourse- Garside structure and Dehornoy ordering of braid groups for topologists II - Tetsuya Ito, Kyoto University11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 5:00pm EDTBraids and combinatorial knot Floer homology - Shea Vela-Vick, Louisiana State University11th Floor Lecture Hall
Friday, August 8, 2014
TimeEventLocationMaterials
8:30 - 9:30am EDTKnot Floer homologies - Andras Stipsicz, Hungarian Academy of Sciences (MTA)11th Floor Lecture Hall
9:45 - 10:45am EDTCombinatorial tangle Floer homology - Ina Petkova, Rice University11th Floor Lecture Hall
10:45 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00pm EDTComputational Problem Session - John Baldwin, Boston College11th Floor Lecture Hall 
12:00 - 1:15pm EDTBreak for Lunch  
1:15 - 2:15pm EDTMonoids, braids and the mapping class group - John Etnyre, Georgia Institute of Technology11th Floor Lecture Hall 
2:30 - 3:30pm EDTSpectral Sequence from Khovanov Homology - Sucharit Sarkar, Princeton University11th Floor Lecture Hall

Lecture Videos

Knot Floer homologies

Andras Stipsicz
Hungarian Academy of Sciences (MTA)
August 8, 2014