Entrance hall of the ICMS

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)
Michel Kervaire

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 2k-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)
The magic square and the Kervaire invariant

11.00 - 11.45

Coffee and tea served in the Chapterhouse

11.45 - 12.45

Michael Hopkins (Harvard University)
The Kervaire invariant: guide to the obstructions

12.45 - 14.30

Lunch served in the Chapterhouse

14.30 - 15.30

John Jones (University of Warwick)
The search for framed manifolds with Kervaire invariant one

15.30 - 16.30

Coffee and tea served in the Chapterhouse

16.30 - 17.30

Erik Pedersen (University of Copenhagen)
H-spaces and the Kervaire invariant

18.00 - 19.00

Wine reception at the Informatics Forum


Tuesday 26 April

09.30 - 10.30

Jack Morava (Johns Hopkins University)
HHR's equivariant cohomology theory and Abelian varieties Link to slides (external)

10.30 - 11.30

Coffee and tea served in the Chapterhouse

11.30 - 12.30

Doug Ravenel (University of Rochester)
Outline of the proof Link to slides or Link to concise version of slides

12.30 - 14.00

Lunch

14.00 - 15.00

John Greenlees (University of Sheffield)
Equivariant stable homotopy theory and ordinary cohomology

15.15 - 16.15

Mark Mahowald (Northwestern University)
The role of KI classes in homotopy

16.15 - 17.00

Coffee and tea served in the Chapterhouse

17.00 - 18.00

Jean Lannes (École Polytechnique)
Remakes of Browder's paper on the Kervaire invariant Link to slides


Wednesday 26 April

09.30 - 10.30

Mike Hill (University of Virginia)
The slice filtration

10.30 - 11.30

Coffee and tea served in the Chapterhouse

11.30 - 12.30

Peter Akhmetev (Izmiran)
A geometric approach to stable homotopy groups of spheres: The Kervaire invariant Link to slides

12.30 - 14.00

Lunch

 


Free afternoon

17.30


ICMS closing time


Thursday 28 April

09.30 - 10.30

Stefan Schwede (University of Bonn)
Ultra-commutative ring spectra

10.30 - 11.30

Coffee and tea served in the Chapterhouse

11.30 - 12.30

Robert Bruner (Wayne State University)
Classical approaches to Kervaire classes Link to slides (external)

12.30 - 14.00

Lunch

14.00 - 15.00

Tilman Bauer  (University of Amsterdam)
The periodicity theorem

15.15 - 16.15

Hans-Werner Henn (Université de Strasbourg)
The chromatic splitting conjecture; the case of the prime 3 and chromatic level 2

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)
Tambura functions

10.30 - 11.30

Coffee and tea served in the Chapterhouse

11.30 - 12.30

Hal Sadofsky (University of Oregon)
The detection theorem Link to slides

12.30 - 14.00

Lunch

14.00 - 15.00

Doug Ravenel (University of Rochester)
The gap theorem Link to slides

15.15 - 16.15

Tyler Lawson (University of Minnesota)
Relative Picard and Brauer groups for S-algebras

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 Down
Atiyah, Sir Michael
The magic square and the Kervaire invariant
View Abstract Down
Bauer, Tilman
The periodicity theorem
View Abstract Down
Bruner, Robert
Classical approaches to Kervaire classes
View Abstract Down
Greenlees, John
Equivariant stable homotopy theory and ordinary cohomology
View Abstract Down
Jones, John
The search for framed manifolds with Kervaire invariant one
View Abstract Down
Lannes, Jean
Remakes of Browder's paper on the Kervaire invariant
View Abstract Down
Lawson, Tyler
Relative Picard and Brauer groups
View Abstract Down
Mahowald, Mark
The role of the KI classes in homotopy
View Abstract Down
Morava, Jack
HHR's equivariant cohomology theory and abelian varieties
View Abstract Down
Ravenel, Douglas
Talk 1: "Outline of the proof" Talk 2: "The gap theorem"
View Abstract Down
Sadofsky, Hal
The Detection Theorem
View Abstract Down
Schwede, Stefan
Ultra-commutative ring spectra
View Abstract Down

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 Heinrich-Heine-Universität Düsseldorf
Tangora, Martin University of Illinois at Chicago
Theriault, Stephen University of Aberdeen
Ullman, Harry University of Sheffield
Zare, Hadi The University of Manchester