May 18, 2021

Homotopy Theory Program

During 1995-96 the Fields Institute is sponsoring an emphasis year in homotopy theory. The main period of activity for the program has just begun and will run until the beginning of June. The organizing committee for the program consists of: W.Dwyer (University of Notre Dame), S.Halperin (University of Toronto), R.Kane (University of Western Ontario), S.Kochman (York University), D.Ravenel (University of Rochester) and P.Selick (University of Toronto).
All activities are taking place at the new permanent site of the Fields Institute at the University of Toronto.
What follows is information concerning various aspects of the homotopy program which will be offered after the current January stable homotopy emphasis session ends.


    • weekly program colloquium
    • regular research and graduate seminars
    • lecture series concerning the application of homotopy theory to other disciplines

  • February-April
    • Graduate Course: Classifying spaces and cohomology operations
    • Graduate Course: Differential algebras, rational and mod p homotopy theory

  • Feb-May: Poincare Series of Lectures

  • March 2-3: K-theory meeting

  • April 19-22: workshop on interaction between homotopy, geometry and physics
  • May 13-June 7: Emphasis session in unstable homotopy theory, including two one-week workshops. These workshops will take place during
    • May 27-31 (Unstable Homotopy)
    • June 3-7 (Rational Homotopy)

Graduate Courses

What follows are course descriptions of the graduate courses to be offered during the January-April 1996. Each course will meet once a week, either on a Wednesday afternoon or a Thursday morning, for approximately 12 weeks.

  • Classifying Spaces and Cohomology Operations
    • Instructor: Richard Kane
    • Schedule: 10:30-12:30, Wednesdays; January 24 - April 17, 1996
    Course will focus on the use of invariant theory in understanding the cohomology of classifying spaces: invariant theory and pseudo- reflection groups, mod p polynomial cohomology algebras, the Lannes T functor, homotopy fixed point theory, Dwyer-Wilkerson study of p compact groups, homotopy colimit decompositions of classifying spaces

  • Differential Algebras, Rational and Mod p Homotopy Theory
    • Instructor: Steve Halperin
    • Schedule: 10-12 am, Thursdays; January 25 - April 18, 1996
    Differential graded algebras and modules over a DGA,semi-free resolutions, chain algebras for loop spaces and their Adams-Hilton models, cochain algebras for spaces and their T(V)-models, commutative cochain algebras and their Sullivan models, the model of a finite complex, Lusternik-Schnirelmann category of spaces and models, application to the homology algebra of a loop space of a finite complex


  • Emphasis Session in Stable Homotopy Theory
    • Organizer: Stan Kochman
    • Dates: January 2-26, 1996
    The major activity is a workshop during the week of January 15-19. A number of expositional lecture series and seminars during the other weeks are also taking place.

  • Algebraic K-Theory conference
    • Organizer: Rick Jardine
    • Dates: March 2-3, 1996
    This conference is the second annual Great Lakes K-theory conference. Besides the 2 day weekend conference, there will also be additional expositional lectures on the days before and/or after the conference.

  • Workshop in Homotopy, Geometry and Physics
    • Organizers: Jacques Hurtubise and Richard Kane
    • Dates: April 19-22, 1996
    This conference will focus on the use of homotopy theory in understanding problems related to geometry and physics

  • Emphasis Session in Unstable Homotopy
    • Organizers: Steve Halperin, Richard Kane, Paul Selick
    • Dates: May 13 - June 7, 1996
    The major activities will be workshops in unstable homotopy theory during the week of May 27-31 and in rational homotopy theory during the week of June 3-7. A number of expositional lectures and seminars will take place in the weeks preceeding these workshops.