Entrance hall of the ICMS Workshop

Braids in algebra, geometry and topology

May 22, 2017 - May 26, 2017

ICMS, 15 South College Street

Organisers

Name Institution
Brendle, Tara University of Glasgow
Ellenberg, Jordan University of Wisconsin
Putman, Andrew University of Notre Dame
Ranicki, Andrew University of Edinburgh

Workshop group photographs available via our Flickr account.

 

Braids are a classical object of study in mathematics and physics. One often first thinks of a braid geometrically, in the sense of “plaits", with a natural group structure. Braids also describe the configuration space of points in a disk or plane; this in turn can be viewed as the space of roots of polynomials over the complex numbers. Hence braids play a prominent role in a wide variety of disciplines including knot theory and low-dimensional topology, number theory, algebraic geometry, geometric group theory, algebraic topology, and mathematical physics. Braid groups also play a huge role in many applied areas such as cryptography, robotics, fluid dynamics, and molecular biology.

The purpose of this workshop is to celebrate the breadth of the topic, with an eye on identifying common problems that admit multiple phrasings and multiple approaches. We will foster collaborations who may use algebro-geometric techniques to solve a problem in braid groups, for example, but we will also promote the use of braids as a common currency through which, say, a problem in algebraic geometry could be solved using techniques from one of the other fields listed above. Our aim is to ensure that a variety of viewpoints on the subject remains a shared experience for practitioners in a variety of fields, at all career stages.

The organisers gratefully acknowledge the financial support from the Glasgow Mathematical Journal Learning and Research Support Fund; the Heilbronn Institute for Mathematical Research, the National Science Foundation and the Edinburgh Mathematical Society.

 


Arrangements

Participation

  • Invited participants received an email invitation from ICMS.

Venue
The workshop will be held at ICMS, 15 South College Street, Edinburgh. 

UK Visas
If you are travelling from overseas you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and if so how to apply for one. 

Travel
Information about travel to the UK and Edinburgh is available here.

Please note that it is your responsibility to have adequate travel insurance to cover medical and other emergencies (volcanic ash disruptions) that may occur on your trip.

A taxi directly from the airport will cost approximately 20.00 to 25.00 GBP to the city centre for a one-way journey.     There is also a bus service direct from the airport to the city centre which will cost 4.50 GBP single or 7.50 GBP return - the Airlink 100.  This is a frequent service (every 10 minutes during peak times) and will bring you close to Waverley Railway Station, only a short walk to the accommodation and the workshop venue (see map in 'Venue' section above). 

Lothian buses charge £1.60 for a single, £4.00 for a day ticket. Please note that the exact fare is required and no change is given.

If travelling by train, please note that Edinburgh has several railway stations - Waverley Railway Station being the main station and closest to the workshop venue at 15 South College Street.  If you alight at Edinburgh Waverley, the workshop venue is an easy 10 minute walk over North and South Bridge. The second large railway station is called Haymarket and is at the West End of the city centre.    Please be aware that there is also an Edinburgh Park railway station but this is at the west side of the city some way from the city centre.  For ICMS, use Edinburgh Waverley.

 

Programme

This is a provisional programme and may be subject to alteration.

You may download the abstracts for the workshop here.  

Monday 22 May 2017 

09:00-10:00

Registration & coffee/tea in the Chapterhouse, Level 1

10:00-10:10

Welcome/opening

10:15-11:00

Dan Margalit (Georgia Institute of Technology)
Hyperelliptic Torelli Groups: problems and progress

11:15-12:00

Richard Hepworth (University of Aberdeen)
The edge of the stable range

12:00-13:30

Lunch in the Chapterhouse, Level 1

13:30-14:15

Nigel Boston (University of Wisconsin-Madison)
Random Galois groups and pro-p braid groups

14:30-15:15

Luis Paris (Université de Bourgogne)
Endomorphisms of the mapping class group of a non-orientable surface

15:15-15:45

Coffee/tea in the Chapterhouse, Level 1

15:45-16:30

Mitchell Berger (University of Exeter)
Applications of braids in dynamics and solar physics

16:45-17:30

Benson Farb (University of Chicago)
Braids, polynomials and Hilbert's (still open) 13th problem

17:30-19:00

Informal wine reception in the Chapterhouse, Level 1

 

Tuesday 23 May 2017

10:00-10:45

Eli Grigsby (Boston College)
Braids and homology-type invariants

10:45-11:15

Coffee/tea in the Chapterhouse, Level 1

11:15-12:00

David Roberts (University of Minnesota, Morris) 
Monodromy of Hurwitz-Belyi maps

12:15-13:00

Joan Birman (Columbia University)
Computing distance in the curve graph

13:00-14:30

Lunch provided in the Chapterhouse, Level 1

14:30-15:15

Alexandru Suciu (Northeastern University)
Algebraic invariants of pure braid-like groups

15:20-16:15

Lightning talks
Becca Winarski
(University of Wisconsin-Milwaukee)
Rachael Boyd (University of Aberdeen)
Benjamin Knudsen (Harvard University)
Jesse Wolfson (University of Chicago)
Megan Maguire (University of Wisconsin-Madison)
Balazs Strenner (Georgia Institute of Technology)
Diana Hubbard (University of Michigan)
Weiyan Chen (University of Chicago)

16:15-16:45

Coffee/tea in the Chapterhouse, Level 1

16:45-17:30

TN Venkataramana (Tata Institute of Fundamental Research)
Burau representation and arithmetic groups

18:15-19:15

doors open to public: 17.45
Public lecture by Benson Farb (University of Chicago)
Polynomials, braids and you
followed by informal wine reception in the Chapterhouse, Level 1, 19.15 - 20.15  


Wednesday 24 May 2017

10:00-10:45

Nathalie Wahl (University of Copenhagen)
Polynomiality for braid group representations

10:45-11:15

Coffee/tea in the Chapterhouse, Level 1

11:15-12:00

Craig Westerland (University of Minnesota)
Fox-Neuwirth/Fuks cells, quantum shuffle algebras, and Malle’s conjecture for function fields

12:15-13:00

Jean-Luc Thiffeault (University of Wisconsin)
Topological optimization with braids 

13:00-13.05

Group photograph to be taken at the front entrance

13:05 onwards

Free afternoon  

 

Thursday 25 May 2017

10:00-10:45

Martin Bridson (University of Oxford)
Kahler groups, RAAGs and subdirect products of surfaces

10:45-11:15

Coffee/tea in the Chapterhouse, Level 1

11:15-12:00

Eriko Hironaka (Florida State University)
Braid actions on rational maps

12:15-13:00

Ivan Marin (Université d'Amiens)
Braids, ties, and Hecke algebras  

13:00-14:30

Lunch in the Chapterhouse, Level 1

14:30-15:15

Problem session

15:20-16:15

Lightning talks
Neil Fullarton
(Rice University)
Celeste Damiani (Osaka City University)
Alan McLeay (University of Glasgow)
Tyrone Ghaswala (University of Waterloo/Manitoba)
Corey Bregman (Rice University/Brandeis)
Lei Chen (University of Chicago)
Alan Logan (University of Glasgow)
Nick Salter (University of Chicago)

16:15-16:45

Coffee/tea in the Chapterhouse, Level 1

16:45-17:30

Robert Ghrist (University of Pennsylvania)
Morse theory on spaces of braids

17:30-19:00

Free time 

19:00

Workshop dinner in the St Trinnean's Room, St Leonard's Hall, Pollock Halls 

 

Friday 26 May 2017

10:00-10:45

Karen Vogtmann (University of Warwick)
Homology stability for braid groups and mapping class groups 

10:45-11:15

Coffee/tea in the Chapterhouse, Level 1

11:15-12:00

Gregor Masbaum (CNRS)
An application of TQFT to modular representation theory

12:15-13:00

Dale Rolfsen (University of British Columbia)
Braids, Aut(F_n) and small volume hyperbolic 3-manifolds

13.00

Close of workshop

 

You may download the abstracts for the workshop here.   

 

Presentations:

Presentation Details
Berger, Mitchell
Applications of braids in dynamics and solar physics
View Abstract Down
Birman, Joan
Computing distance in the curve graph
View Abstract Down
Boston, Nigel
Random Galois groups and pro-p braid groups
View Abstract Down
Boyd, Rachael
Homological stability for families of Artin groups
View Abstract Down
Bregman, Corey
Hyperelliptic graphs and the Jacobian map on outer space
View Abstract Down
Bridson, Martin
Kahler groups, RAAGs and subdirect products of surfaces
View Abstract Down
Chen, Lei
Surjective homomorphisms between surface braid groups
View Abstract Down
Chen, Weiyan
Homology of braid group with coefficients in the Burau representation
View Abstract Down
Damiani, Celeste
Loop braid groups: ubiquitous objects opening the door to a plethora of questions through different fields.
View Abstract Down
Farb, Benson
Braids, polynomials and Hilbert's (still open) 13th problem
View Abstract Down
Fullarton, Neil
Top-dimensional cohomology in the mapping class group
View Abstract Down
Ghaswala, Tyrone
Braids embedded in mapping class groups
View Abstract Down
Ghrist, Robert
Morse Theory on Spaces of Braids
View Abstract Down
Grigsby, Julia Elisenda
Braids and homology-type invariants
View Abstract Down
Hepworth, Richard
The edge of the stable range
View Abstract Down
Hironaka, Eriko
Braid actions on rational maps
View Abstract Down
Hubbard, Diana
An invariant of closed braids from the Khovanov setting
View Abstract Down
Knudsen, Benjamin
Homology of surface and graph braid groups
View Abstract Down
Maguire, Megan
Cohomology algebras of conguration spaces
View Abstract Down
Margalit, Dan
Hyperelliptic Torelli Groups: Problems and Progress
View Abstract Down
Marin, Ivan
Braids, Ties, and Hecke algebras
View Abstract Down
Masbaum, Gregor
An application of TQFT to modular representation theory
View Abstract Down
McLeay, Alan
Ivanov’s metaconjecture and complexes of regions.
View Abstract Down
Paris, Luis
Endomorphisms of the mapping class group of a non-orientable surface
View Abstract Down
Roberts, David
Monodromy of Hurwitz-Belyi maps
View Abstract Down
Rolfsen, Dale
Braids, Aut(F_n) and small volume hyperbolic 3-manifolds
View Abstract Down
Salter, Nick
Mapping class groups and monodromy of families of plane curves
View Abstract Down
Strenner, Balazs
Fast Nielsen-Thurston classification
View Abstract Down
Suciu, Alexandru
Algebraic invariants of pure braid-like groups
View Abstract Down
Thiffeault, Jean-Luc
Topological optimization with braids
View Abstract Down
Venkataramana, T.N.
Burau representation and arithmetic groups
View Abstract Down
Vogtmann, Karen
Homology stability for braid groups and mapping class groups
View Abstract Down
Wahl, Nathalie
Polynomiality for braid group representations
View Abstract Down
Westerland, Craig
Fox-Neuwirth/Fuks cells, quantum shuffle algebras, and Malle’s conjecture for function fields
View Abstract Down
Winarski, Becca
Lifting homeomorphisms of branched covers of spheres
View Abstract Down
Wolfson, Jesse
Coincidences of homological densities, predicted by arithmetic
View Abstract Down

Participants

Name Institution
Bartel, Alex Warwick University
Bellingeri, Paolo Université de Caen
Berger, Mitchell University of Exeter
Birman, Joan Columbia University
Boston, Nigel University of Wisconsin-Madison
Boyd, Rachael University of Aberdeen
Bregman, Corey Rice University
Brendle, Tara University of Glasgow
Bridson, Martin University of Oxford
Chen, Lei University of Chicago
Chen, Weiyan University of Chicago
Ciobanu, Laura Heriot-Watt University
Damiani, Celeste Osaka City University
Farb, Benson University of Chicago
Fullarton, Neil Rice University
Gadre, Vaibhav University of Glasgow
Ghaswala, Tyrone University of Waterloo
Ghrist, Robert University of Pennsylvania
Grigsby, Julia Elisenda Boston College
Hepworth, Richard University of Aberdeen
Hironaka, Eriko Florida State University
Hornig, Gunnar University of Dundee
Howie, Jim Heriot-Watt University
Hubbard, Diana University of Michigan
Jeffreys, Luke University of Glasgow
Kahrobaei, Delaram City University of New York
Kedra, Jarek University of Aberdeen & University of Szczecin
Knudsen, Benjamin Harvard University
Koberda, Thomas University of Virginia
Lebed, Victoria Trinity College Dublin
Licata, Tony Australia National University
Logan, Alan University of Glasgow
Maguire, Megan University of Wisconsin-Madison
Margalit, Dan Georgia Institute of Technology
Marin, Ivan Université d'Amiens
Masbaum, Gregor CNRS
McLeay, Alan University of Glasgow
Paris, Luis Université de Bourgogne
Putman, Andrew University of Notre Dame
Ranicki, Andrew University of Edinburgh
Roberts, David University of Minnesota
Rolfsen, Dale University of British Columbia
Salter, Nick University of Chicago
Strenner, Balazs Georgia Institute of Technology
Suciu, Alexandru Northeastern University
Szymik, Markus NTNU Norwegian University of Science and Technology
Thiffeault, Jean-Luc University of Wisconsin
Venkataramana, T.N. Tata Institute of Fundamental Research
Vogtmann, Karen University of Warwick
Wahl, Nathalie University of Copenhagen
Wemyss, Michael University of Glasgow
Westerland, Craig University of Minnesota
Winarski, Becca University of Wisconsin-Milwaukee
Wolfson, Jesse The University of Chicago