Title: Homotopy theory, derived functors, and Bousfield-Kan completion
Speaker: John Harper (OSU)
Abstract: We will introduce some basic ideas of algebraic topology and simplicial homotopy theory with an emphasis on derived functors in topological contexts (e.g., homotopy limits and homotopy colimits). We will illustrate these ideas with some recent results on Bousfield-Kan completion (the idea of iterating a comparison map to build a cosimplicial resolution of a space out of simpler pieces that throw away information). The main result is that certain mild connectivity assumptions lead to strong convergence of the (spectral sequence associated to the tower of) the resolution of the original space.
Note: This is part of the Invitations to Mathematics lecture series given each year in Autumn Semester. Pre-candidacy PhD students can sign up for this lecture series by registering for one or two credit hours of Math 6193 with Professor Nimish Shah.