Summary

This course will seek to answer the question, “What is duality in homotopy theory?” We will discuss many named forms, including for instance, Poincaré, Alexander, Lefschetz, Pontrjagin, Spanier-Whitehead, Hodge, Vogell, Ranicki, Whitney, Serre, Eckmann-Hilton, Atiyah, Brown-Comenetz, Gross-Hopkins, and Gorenstein duality, as well as the relationships among them.

The class meeting format will consist of a fifty minute lecture, followed by a short break and an additional twenty minutes for participant discussion of suggested exercises. Six exercises will be selected for students to turn in written solutions at the end of the course as a written problem portfolio assignment.

Participant expectations

Each student is expected to participate fully in the course, just as if it were an in-person course at the student’s home institution. Students are expected to attend class meetings, including the discussion portion, and complete a six problem written solution portfolio before the end of the course. The workload outside of course meeting times will be minimal.

As a general rule, students are expected to obtain 2-3 independent study credits from their home universities for their participation in the course. At the end of the semester, a grade of A/B/C/Fail will be reported to each student’s home institution advisor.

Prerequisites

A basic familiarity with spectra is desired. The intended audience for this course is (likely) second year graduate students and beyond.

Instructors

Sarah Petersen (University of Colorado) is the lead instructor. Graduate students to be named will serve as graduate teaching assistants.

Application

Please submit the application form to apply. Applications received by August 19 will receive full consideration. Unfortunately, space is limited, and we may not be able to accept all qualified applicants.

Schedule

The course meets on Mondays and Wednesdays at 11:00-12:20 eastern time, starting August 27 and ending on December 12. The week of November 26 will be a break.