Asilata Bapat (ANU) will be speaking in the algebra seminar next week. We will go out for lunch after the talk. When: Friday 24 May, 12-1pm Where: SMRI seminar room (Macleay Building (A12) room 301) Title: A combinatorial study of Harder--Narasimhan filtrations Abstract: A choice of a stability condition on a category gives rise to a canonical filtration of any object, with semistable factors. This is called the Harder--Narasimhan (HN) filtration. Under suitable assumptions, the possible HN filtration factors of an object are highly and non-trivially constrained. Furthermore, these possible "HN support sets" have a rich combinatorial structure. In this talk, I will elaborate on some of these ideas.