Hopkins Talk #1: Stacks and Complex Oriented Cohomology Theories

This is the first in a series of lectures given by Mike Hopkins at the Talbot workshop in April of 2007. For this talk, Mike was asked to talk about “the tmf theorem” and to explain some of the motivation and intuition behind the stacky language. As those who have heard him speak know, Mike is a very entertaining lecturer. Sadly, these notes reflect only the mathematical content of his talks, leaving the many funny comments and laughter in the memories of the audience. All of the content that follows is taken essentially directly from Mike’s talk. We have expanded very slightly some portions and we have reorganized some of the material, and we take full responsibility for any mathematical or typographical errors.