Hi everyone, There has been a plan in place for some weeks of Benno van den Berg visiting USPN while he is visiting Paris next week. We have selected the unusual time of 1pm on Tuesday 20/10; see the title and abstract below. Provisionally I have booked a room on the 4th floor of the MathSTIC building for this purpose; please call or text me on 0635326197 if you need help getting into the university or the building. _It is of course possible that we will have to cancel this at short notice_, either because the university is completely closed or because only staff will be allowed inside. Since the president of the university doesn't tend to officially decide these things until the evening before, I'll send another message on Monday based on that. Otherwise, see you there. Best wishes, Morgan ---- Title: Algebraic weak factorisation systems Abstract: Weak factorisation systems (WFSs) play an important role in abstract homotopy theory; in particular, Quillen model structures consist of two WFSs that interact in a good way. A WFS on a category consists of two classes maps, let's call them left and right maps, such that any map factors as a left map followed by a right map and the two classes determine each other through lifting properties. Algebraic weak factorisation systems (AWFSs, due to Grandis, Tholen and Garner) are a more explicit version of these WFSs in that both the factorisation and the lifts are part of the structure of a WFS; in particular, the property of being a left (or right) map is replaced by a notion of having the structure of a left (or right) map. Every AWFS determines a WFS, but at the same time there are also situations that can be seen as instances of an AWFS, but not as a WFS. Much of the recent interest in AWFSs comes from homotopy type theory, as many of the recent attempts to give a constructive semantics for homotopy type theory have made heavy use of the theory of AWFs. In this talk I will gave an overview of the theory of AWFs, stressing the relation with double categories. I will also discuss joint work with Lingyuan Ye, John Bourke and Ellie Lohman on monoidal AWFSs and distributive laws for AWFSs.