The Kervaire invariant and stable homotopy theory
Apr 25, 2011 - Apr 29, 2011
15 South College Street, Edinburgh EH8 9AA
Organisers
Name | Institution |
---|---|
Greenlees, John | University of Sheffield |
Hopkins, Mike | Harvard University |
Ranicki, Andrew | University of Edinburgh |
Strickland, Neil | University of Sheffield |
Michel Kervaire (1927-2007)
At the 2009 Atiyah80 ICMS Workshop Hill, Hopkins and Ravenel announced a proof that there do not exist manifolds with Kervaire invariant 1 in dimensions 2^{k}-2 for any k≥8. This solved the long standing open Kervaire invariant problem (except for dimension 126, the only dimension which now remains open), which has been of central importance in homotopy theory for over 40 years.
The principal objective of the workshop is to disseminate the methods used in the solution of the Kervaire invariant conjecture, and the use of equivariant and motivic methods more generally. It is also hoped to assess the prospects for using the methods to prove structural results about stable homotopy, and to report on progress which will have taken place by the time of the meeting.
Doug Ravenel has a website dedicated to the Kervaire invariant problem, with further information about the 2009 announcement and subsequent developments.
Invited speakers:
P.Akhmetev (Izmiran, Troitsk)
M.Atiyah (Edinburgh)
R.Bruner (Wayne State)
M.Hill (Virginia)
M.Hopkins (Harvard)
J.Jones (Warwick)
J.Lannes (Ecole Polytechnique)
T.Lawson (Minnesota)
M.Mahowald (Northwestern)
J.Morava (Johns Hopkins)
E.Pedersen (Copenhagen)
D.Ravenel (Rochester)
S.Schwede (Bonn)
Arrangements
Participation
All places have been allocated.
Venue
The workshop will take place in the Newhaven lecture theatre at ICMS, 15 South College Street, Edinburgh, Scotland.
Lecture theatre facilities
The lecture theatre is fitted with data projection, visualiser (the new generation of over-head), smart-board and blackboard. Speakers may wish to note that since the lectures will be filmed, it is inadvisable to use blackboards as presentation medium simply because they don't come out clear on film. Please use alternative methods. Please also note that blackboard and data projection cannot be used simultaneously. More information about this is available form Helene Frossling.
Accommodation
Accommodation has been booked for all delegates who are not based in Edinburgh. Participants who wish to make use of this booking must inform Helene Frossling of their dates of travel. Accommodation booked by ICMS will be paid for by the workshop grants, apart from any costs incurred by changing bookings from single to double occupancy. DELEGATES WILL BE INFORMED OF THE NAME AND ADDRESS OF THEIR ALLOCATED ACCOMMODATION SOMETIME BETWEEN 7 AND 12 APRIL.
Posters
All participants are welcome to present posters during the workshop. Poster boards will be available throughout the week in the Chapterhouse where all catering will be served. It will therefore be easy to display posters as well as provide feedback on other people's posters throughout the week. Please note that the poster boards are big enough for sizes A0 PORTRAIT or A1 LANDSCAPE. Velcro is the only option for hanging the posters but there is plenty on site.
Visas
Attendees may need to apply for a visa to enter the UK. This government website gives more information.
Conference Co-ordinator
Helene Frossling is the conference co-ordinator for this workshop.
Programme
Programme published 1 April 2011.
Monday 25 April
09.00 - 09.55 | Registration and coffee/tea |
09.55 - 10.00 | Welcome & Health and Safety information |
10.00 - 11.00 | Michael Atiyah (University of Edinburgh) |
11.00 - 11.45 | Coffee and tea served in the Chapterhouse |
11.45 - 12.45 | Michael Hopkins (Harvard University) |
12.45 - 14.30 | Lunch served in the Chapterhouse |
14.30 - 15.30 | John Jones (University of Warwick) |
15.30 - 16.30 | Coffee and tea served in the Chapterhouse |
16.30 - 17.30 | Erik Pedersen (University of Copenhagen) |
18.00 - 19.00 | Wine reception at the Informatics Forum |
Tuesday 26 April
09.30 - 10.30 | Jack Morava (Johns Hopkins University) |
10.30 - 11.30 | Coffee and tea served in the Chapterhouse |
11.30 - 12.30 | Doug Ravenel (University of Rochester) |
12.30 - 14.00 | Lunch |
14.00 - 15.00 | John Greenlees (University of Sheffield) |
15.15 - 16.15 | Mark Mahowald (Northwestern University) |
16.15 - 17.00 | Coffee and tea served in the Chapterhouse |
17.00 - 18.00 | Jean Lannes (École Polytechnique) |
Wednesday 26 April
09.30 - 10.30 | Mike Hill (University of Virginia) |
10.30 - 11.30 | Coffee and tea served in the Chapterhouse |
11.30 - 12.30 | Peter Akhmetev (Izmiran) |
12.30 - 14.00 | Lunch |
| Free afternoon |
17.30 | ICMS closing time |
Thursday 28 April
09.30 - 10.30 | Stefan Schwede (University of Bonn) |
10.30 - 11.30 | Coffee and tea served in the Chapterhouse |
11.30 - 12.30 | Robert Bruner (Wayne State University) |
12.30 - 14.00 | Lunch |
14.00 - 15.00 | Tilman Bauer (University of Amsterdam) |
15.15 - 16.15 | Hans-Werner Henn (Université de Strasbourg) |
16.15 - 17.00 | Coffee and tea served in the Chapterhouse |
19.00 - 23.30 | Conference dinner. Served in the Pentland suite at the John McIntyre Centre, Pollock Halls |
Friday 29 April
09.30 - 10.30 | Neil Strickland (University of Sheffield) |
10.30 - 11.30 | Coffee and tea served in the Chapterhouse |
11.30 - 12.30 | Hal Sadofsky (University of Oregon) |
12.30 - 14.00 | Lunch |
14.00 - 15.00 | Doug Ravenel (University of Rochester) |
15.15 - 16.15 | Tyler Lawson (University of Minnesota) |
16.15 - 17.00 | Coffee and tea served in the Chapterhouse |
Presentations:
Presentation Details | |
---|---|
Akhmetev, Peter | |
Geometric approach to stable homotopy groups of spheres: The Kervaire invariant. | |
View Abstract | |
Atiyah, Sir Michael | |
The magic square and the Kervaire invariant | |
View Abstract | |
Bauer, Tilman | |
The periodicity theorem | |
View Abstract | |
Bruner, Robert | |
Classical approaches to Kervaire classes | |
View Abstract | |
Greenlees, John | |
Equivariant stable homotopy theory and ordinary cohomology | |
View Abstract | |
Jones, John | |
The search for framed manifolds with Kervaire invariant one | |
View Abstract | |
Lannes, Jean | |
Remakes of Browder's paper on the Kervaire invariant | |
View Abstract | |
Lawson, Tyler | |
Relative Picard and Brauer groups | |
View Abstract | |
Mahowald, Mark | |
The role of the KI classes in homotopy | |
View Abstract | |
Morava, Jack | |
HHR's equivariant cohomology theory and abelian varieties | |
View Abstract | |
Ravenel, Douglas | |
Talk 1: "Outline of the proof" Talk 2: "The gap theorem" | |
View Abstract | |
Sadofsky, Hal | |
The Detection Theorem | |
View Abstract | |
Schwede, Stefan | |
Ultra-commutative ring spectra | |
View Abstract |
Participants
Name | Institution |
---|---|
Adamaszek, Michal | University of Warwick |
Adams-Florou, Spiros | University of Edinburgh |
Akhmetev, Peter | IZMIRAN |
Atiyah, Sir Michael | University of Edinburgh |
Baker, Andrew | University of Glasgow |
Barnes, David | The University of Sheffield |
Barthel, Tobias | University of Oxford |
Bauer, Tilman | VU University Amsterdam |
Brito, Pedro | University of Aberdeen |
Bruner, Robert | Wayne State University |
Cazanave, Christophe | University of Nice |
Chacholski, Wojciech | KTH |
Cheung, Pokman | University of Sheffield |
Collins, Julia | University of Edinburgh |
Cranch, James | University of Leicester |
Crowley, Diarmuid | Hausdorff Research Institute for Mathematics |
Garcia Pulido, Ana Lucia | University of Warwick |
Garkusha, Grigory | Swansea University |
Gasparim, Elizabeth | University of Edinburgh |
Gepner, David | University of Regensburg |
Grant, Mark | The University of Edinburgh |
Gray, Brayton | Univerity of Illinois at Chicago |
Greenlees, John | University of Sheffield |
Henn, Hans-Werner | IRMA, Université de Strasbourg |
Hill, Michael | University of Virginia |
Hopkins, Mike | Harvard University |
Hubbuck, John | University of Aberdeen |
Husemoller, Dale | Max Planck Institute for Mathematics |
Joachim, Michael | Westfälische Wilhelms-Universität |
Jones, John | University of Warwick |
Kedziorek, Magdalena | University of Sheffield |
Lam, Kee Yuen | University of British Columbia |
Lam, S.P. | University of Cambridge |
Lannes, Jean | Ecole Polytechnique |
Lawson, Tyler | University of Minnesota |
Lesh, Kathryn | Union College |
Levikov, Filipp | University of Aberdeen |
Mahowald, Mark | Northwestern University |
Malhotra, Arjun | University of Sheffield |
McTague, Carl | University of Southampton |
Meier, Lennart | Universität Bonn |
Morava, Jack | The Johns Hopkins University |
Noel, Justin | Max Planck Institute for Mathematics |
Nogami, Jumpei | Universität Duisburg-Essen |
Oliver, Bob | [permanent address] Universite Paris 13 ; [currently address] Copenhagen University |
Orson, Patrick | University of Durham |
Patchkoria, Irakli | University of Bonn |
Pedersen, Erik Kjær | University of Copenhagen |
Powell, Geoffrey | CNRS and Université Paris 13 |
Randal-Williams, Oscar | University of Cambridge |
Randall, Duane | Loyola University New Orleans |
Ranicki, Andrew | University of Edinburgh |
Ravenel, Douglas | University of Rochester |
RAY, NIGEL | University of Manchester |
Sadofsky, Hal | University of Oregon |
Schwede, Stefan | Universität Bonn |
Strickland, Neil | University of Sheffield |
Swarbrick, Rupert | University of Warwick |
Szymik, Markus | NTNU Norwegian University of Science and Technology |
Tangora, Martin | University of Illinois at Chicago |
Theriault, Stephen | University of Aberdeen |
Ullman, Harry | University of Sheffield |
Zare, Hadi | The University of Manchester |