This volume is the proceedings of the Conference on Homotopy Methods in
Algebraic Topology which took place in Boulder, Colorado from June 20 to June 24,
1999. This was one of the series of AMS-IMS-SIAM Summer Research Conferences
held during the summer of 1999 at the University of Colorado. The organizing
committee consisted of the three editors of this Proceedings, together with Tony
Elmendorf and Jim McClure.
The scientific focus of the conference was on modern aspects of homotopy the-
ory, particularly methods that are being exported to algebraic settings.
This is reflected in the following partial list of topics of the talks: group theory
(e.g. by Rickard, Lewis), set theory (Casacuberta), motivic homotopy (Morel, Hu),
polynomial functors (Dwyer, McCarthy, Arone, Johnson), elliptic curves (Ando,
Hopkins, Mahowald, Rezk), model categories of spectra (Mandell, Karoubi, Ship-
ley), and algebraic K-theory (Madsen, Duflot, Hesselholt). Frank Peterson talked
on the history of cobordism theory, a topic connected to the work of many of our
There were over 100 participants who came from many countries. The 31
speakers reflected this international mix.
The conference coincided with the 60th birthday of University of Chicago Pro-
fessor J. Peter May. It was not coincidence that four of the organizers were students
of Peter, and the fifth a major collaborator. Activities in his honor included a talk
A brief introduction to the work of J. Peter May by Igor Kriz, and a conference
banquet. Among those who attended the conference were 14 of Peter's former
Ph.D. students, 5 current students, and numerous other collaborators and ex Uni-
versity of Chicago instructors. This attests to his extraordinary role as an advisor
over the last quarter century, and to the unwavering enthusiasm and energy he has
brought to the subject. The article by Kriz in this proceedings describes Peter's
wide---ranging and influential research, and includes a recent bibliography.
The conference was primarily supported by the National Science Foundation via
its funding of the Joint Summer Research Conferences. We also wish to thank the
Mathematics Department of the University of Chicago for a generous contribution.
Practical details were smoothly dealt with by the Providence office of the Amer-
ican Mathematical Society and the staff of the University of Colorado. Particular
thanks are due to AMS conference coordinator Donna Salter.
Of course, the success of the conference was due to the participants in general
and the speakers in particular. This conference proceedings is the result of the
efforts of our authors (and referees). To all of you, we offer spirited thanks.