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 Courtesy: John Baldwin

Confirmed Speakers & Participants

Workshop Schedule

Monday, August 4, 2014
TimeEventLocationMaterials
8:30 - 8:55Registration11th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 10:30Minicourse- Braid Foliations I - Doug LaFountain, Western Illinois University11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00Computational complexity of problems in 3-dimensional topology - Nathan Dunfield, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
12:00 - 2:00Break for Lunch  
2:00 - 3:30Minicourse- Nielsen-Thurston theory I - Johanna Mangahas, Brown University11th Floor Lecture Hall 
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 5:00Foliations, Flows, and Contact Structures - Rachel Roberts, Washington University11th Floor Lecture Hall
5:15 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, August 5, 2014
TimeEventLocationMaterials
9:00 - 10:30Minicourse- Braid Foliations II - Doug LaFountain, Western Illinois University11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00Intro. to Legendrian & Transverse Knots - John Etnyre, Georgia Institute of Technology11th Floor Lecture Hall 
12:00 - 2:00Break for Lunch  
2:00 - 3:30Minicourse- Nielsen-Thurston theory II - Joanna Mangahas, Brown University11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 5:00Teichmueller 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 - 10:30Minicourse- Grid Diagrams and Contact Geometry I - Lenhard Ng, Duke University11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00Rectangular Diagrams and Jones' Conjecture I- monotonic simplification and Legendrian links - Ivan Dynnikov, Moscow State University11th Floor Lecture Hall
12:10 - 12:20Group Photo11th Floor Lecture Hall 
12:20 - 2:00Break for Lunch  
2:00 - 3:00Rectangular Diagrams and Jones' Conjecture II- Legendrian graphs, bypasses and simplifying disks - Maxim Prasolov, Moscow State University11th Floor Lecture Hall
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
3:30 - 5:00Minicourse- 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 - 10:30Minicourse- Grid Diagrams and Contact Geometry II - Lenhard Ng, Duke University11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00Divide knots vs L-space knots - Ken Baker, University of Miami11th Floor Lecture Hall
12:00 - 2:00Break for Lunch  
2:00 - 3:30Minicourse- Garside structure and Dehornoy ordering of braid groups for topologists II - Tetsuya Ito, Kyoto University11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 5:00Braids and combinatorial knot Floer homology - Shea Vela-Vick, Louisiana State University11th Floor Lecture Hall
Friday, August 8, 2014
TimeEventLocationMaterials
8:30 - 9:30Knot Floer homologies - Andras Stipsicz, Hungarian Academy of Sciences (MTA)11th Floor Lecture Hall
9:45 - 10:45Combinatorial tangle Floer homology - Ina Petkova, Rice University11th Floor Lecture Hall
10:45 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00Computational Problem Session - John Baldwin, Boston College11th Floor Lecture Hall 
12:00 - 1:15Break for Lunch  
1:15 - 2:15Monoids, braids and the mapping class group - John Etnyre, Georgia Institute of Technology11th Floor Lecture Hall 
2:30 - 3:30Spectral 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