• Our result was first announced on April 21, 2009, in a lecture by Hopkins at the Geometry and Physics: Atiyah80 conference. (This link has some more information.) His title was Applications of algebra to a problem in topology. Here are the slides for that talk; the file is 44MB. There is also a video.
  
  
• I gave four talks on the theorem in Lisbon on May 5-7. Special thanks to Peter Landweber for bringing numerous typos in them to my attention.
  • Lecture 1, May 5, 2009.    Printer friendly version.
    This lecture discusses the work of Kervaire-Milnor on the classification of exotic spheres. Andrew Ranicki's talk on Kervaire's work, given in Geneva in February, with this more recent addendum, is a good online reference for this material. My lecture also includes a brief introduction to the classical Adams spectral sequence.
    

    Frank Adams 1930-1989	Michel Kervaire 1927-2007	John Milnor	Andrew Ranicki

  • Lecture 2, May 6, 2009.    Printer friendly version.
    This lecture covers MU, formal group laws with Quillen's theorem, the Hopkins-Miller theorem, equivariant stable homotopy theory and MU as a C₂ spectrum.

    Peter Landweber	Peter May	Haynes Miller and Frank Peterson	Daniel Quillen

  • Lecture 3, May 7, 2009.    Printer friendly version.
    Covers the homotopy of MU⁽⁴⁾, Postnikov towers, equivariant Postnikov towers, the slice spectral sequence, the gap theorem and RO(G)-graded homotopy.
  • Lecture 4, May 7, 2009.    Printer friendly version.
    Covers geometric fixed points, the slice and reduction theorems, the periodicity and slice differentials theorems, and the homotopy fixed point theorem.
  • Supplement on the Detection Theorem.    Printer friendly version.
  
  
• Mike Hill's talk at the Isle of Skye Conference, June 15, 2009.    Slides    Handout
  
  
• Mike Hopkins' talk at the MIT seminar, July 8, 2009.    Notes by Angelica Osorno.
  
  
• Mike Hill's talk at the MIT seminar, July 15, 2009.    Notes by Angelica Osorno.
  
  
• My talk at the MIT seminar, July 29, 2009.    Slides     Print version
  
  
• My talks in the UR Topology Seminar of September 25 and October 2, 2009.
  • The first lecture is a colloquium style talk designed to be accessible to nontopologists. It includes information about the "World Without End Hypothesis" thought to hold before we proved our theorem.    Slides     Print version
  • The second lecture introduces equivariant spectra and outlines the proof of the Gap Theorem.    Slides     Print version
  
  
• Mike Hopkins' talk at the Mayday Conference, October 16, 2009.
  
  
• Mike Hill's talk at the Mayday Conference, October 18, 2009.
  
  
• My talk at the AMS Special Session on Homotopy Theory at Penn State, October 25, 2009. Slides   Print version   This talk is very similar to the one I gave at UR on September 25.
  
  
• I gave six talks at Tokyo City University on November 4-6, 2009.
  
  • Lecture 1: History and background of the problem.   Slides   Print version  
    
  • Lecture 2: Formal group laws and the Hopkins-Miller theorem.   Slides   Print version  
    
  • Lecture 3: Equivariant stable homotopy theory.    Slides   Print version  
    
  • Lecture 4: The slice spectral sequence and the gap theorem    Slides   Print version  
    
  • Lecture 5: The periodicity theorem.    Slides   Print version  
    
  • Lecture 6: The detection theorem.    Slides   Print version  
    
  
  
  

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Created October 28, 2009; last modified November 4, 2009.