The GEARS seminar

Talia Shlomovich (Heriot-Watt)

Title: Non-planarity of Group Boundaries

Abstract: When can you draw a boundary of a group on a sphere? And when can you not?

In this talk, I aim to convince you that this property is a useful tool for describing and distinguishing between boundaries of groups. This is especially useful for boundaries which are topological fractals, such as Cantor spaces and Menger curves. 

Although non-planar boundaries are common among hyperbolic groups, it is surprisingly difficult to construct them. I will discuss how graph-theoretic characterisations of non-planarity are used to do so, and present certain classes of Coxeter groups as a source of examples. I will then share my progress towards constructing a right-angled Coxeter group with non-planar Morse boundary.

Cassia Edwards (Edinburgh)

Title: Motivating Factorisation Algebras in Quite a Lot of Generality

Abstract: Factorization algebras have been defined in multiple contexts: the manifold setting of Costello-Gwilliam; the chiral algebra setting of Beilinson-Drinfeld and the locally constructible setting of Karlsson-Scheimbauer-Walde. Recently, Barwick has constructed a formalism that seeks to encompass these approaches through the use of twofold symmetric monoidal categories. 

In this talk we will use the definition by Beilinson-Drinfeld to motivate the setting constructed by Barwick, and introduce the starting concepts of his theory - the combinatorics of isolation and isolability spaces.