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Workshop

Hot Topics: Kervaire invariant October 25, 2010 - October 29, 2010
Registration Deadline: October 25, 2010 almost 4 years ago
To apply for Funding you must register by: July 25, 2010 over 4 years ago
Series: Hot Topic
Organizers Mike Hill (University of Virginia), Michael Hopkins (Harvard University), and Douglas C. Ravanel* (University of Rochester)
Speaker(s)

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Description

This workshop will focus on the ideas surrounding the recent solution to the Arf-Kervaire invariant problem in stable homotopy theory by Mike Hill, Mike Hopkins and Doug Ravenel. There will be talks on relevant aspects of equivariant stable homotopy theory, including the norm functor and the slice tower. The pertinent parts of chromatic homotopy theory will be covered including formal groups and formal $A$-modules, the Hopkins-Miller theorem, finite subgroups of Morava stabilizer groups and Ravenel's 1978 solution to the analogous problem at primes bigger than 3. There will also be several talks by the organizers giving a detailed account of the proof of the main theorem. Finally there will be a discussion of the questions raised by the unexpected statement of the theorem.


Accommodations:

A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available.


The cut-off date for reservations is October 11, 2010.


A block of rooms has been reserved at the Hotel Durant. Please mention the workshop name and reference the following code when making reservations via phone, fax or e-mail: MSRIRANDOMMATRIX. If you are making your reservations on line, please go to Hotel Durant website, choose your dates of stay and enter the "123MSRI" promo code in the box. The cut-off date for reservations is September 24, 2010. The rate is $110 per night plus tax.


New, completely renovated Hotel Shattuck Plaza has rooms available for you!


MSRI’s preferred rate is $131. Guests can either call the hotel’s main line, 510-845-7300, and ask for the MSRI rate or go to http://www.hotelshattuckplaza.com, click on "Corporate Rates" in the reservation screen and type the code msri10.


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Schedule
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Oct 25, 2010
Monday
09:25 AM - 09:40 AM
  Welcome
09:40 AM - 10:40 AM
  History of the Kervaire Invariant One Problem
John Jones (University of Warwick)
10:40 AM - 11:10 AM
  Tea
11:10 AM - 12:10 PM
  Construction of the Kervaire Classes
John Jones (University of Warwick)
12:10 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  An Overview of the proof
Douglas Ravenel (University of Rochester)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Introduction to Equivariant Homotopy I
J. May
04:30 PM - 05:50 PM
  Reception
Oct 26, 2010
Tuesday
09:30 AM - 10:30 AM
  Introduction to Equivariant Homotopy II
John Greenlees (University of Sheffield)
10:30 AM - 11:00 AM
  Tea
11:00 AM - 12:00 PM
  Introduction to the Slice Tower: The Slice Theorem
Michael Hill (University of Virginia)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  The Homology of Slice Cells: the Gap Theorem
Teena Gerhardt (Michigan State University)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  The Slice Spectral Sequence for $$C_2$$ and $$C_4$$
Igor Kriz
Oct 27, 2010
Wednesday
09:30 AM - 10:30 AM
  The norm functor and $$MU^{((G))}$$
Haynes Miller (Massachusetts Institute of Technology)
10:30 AM - 11:00 AM
  Tea
11:00 AM - 12:00 PM
  Distinguished Classes in the Underlying Homotopy of $$MU^{((G))}$$
Nitya Kitchloo (Johns Hopkins University)
Oct 28, 2010
Thursday
09:00 AM - 10:00 AM
  Introduction to the Adams-Novikov Spectral Sequence: Ravenel's Proof for Primes > 3
Mark Behrens (Massachusetts Institute of Technology)
10:00 AM - 10:30 AM
  Tea
10:30 AM - 11:30 AM
  Proof of the Detection Theorem
Douglas Ravenel (University of Rochester)
11:30 AM - 12:30 PM
  Differentials in the Slice Spectral Sequence: the Periodicity Theorem
Po Hu (Wayne State University)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Q & A Session
Michael Hill (University of Virginia), Michael Hopkins (Harvard University), Douglas Ravenel (University of Rochester)
03:00 PM - 03:30 PM
  Tea
Oct 29, 2010
Friday
09:30 AM - 10:30 AM
  The Homotopy Fixed Points Theorem
Andrew Blumberg (University of Texas)
10:30 AM - 11:00 AM
  Tea
11:00 AM - 12:00 PM
  From the Reduction Theorem to the Slice Theorem
Daniel Dugger
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Proof of the Reduction Theorem I
Michael Hill (University of Virginia)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Proof of the Reduction Theorem II
Michael Hopkins (Harvard University)