Wednesday November 11
12:00-1:00
Room: Zoom
Ben Cooper (University of Iowa)
Title: A higher categorical homotopy
Abstract: I will discuss a version of higher homotopy in the categorical sense in which homotopies of homotopies are not maps of the same categorical level.
Wednesday December 9
12:00-1:00
Room: Zoom
Anthony Licata (Australia National University)
Title: Group theory in triangulated categories
Abstract: Several classes of groups studied seriously in the last 50 years - mapping class groups of surfaces, automorphism groups of free groups, arithmetic groups,... - share a number of structural similarities. In fact, a useful proof strategy for theorems about one class of groups is sometimes to proceed by analogy, and try to mimic the proof of a known theorem from another class. In this talk I will try to tell you a little bit about another class of groups - the autoequivalence groups of triangulated categories - which seems to share similarities with several of these other classes. The goal will be to introduce some of the important objects in the study of triangulated autoequivalences, and to explain their role by analogy to the theory of mapping class groups. I'll try not to assume much in the way of background, and will spend most of the time talking about the simplest case, when the group in question is the three-strand braid group.