Stacey Law "Sylow restriction in the representation theory of finite groups"

 One of the central themes in the representation theory of finite groups is to understand the relationship between the characters of a finite group G and those of its local subgroups. Following an overview of some of the recent major developments in this area, we will then focus on Sylow branching coefficients. These were introduced to describe the restriction of irreducible characters of G to a Sylow subgroup P of G, and have been recently shown to characterise structural properties such as the normality of P in G. We will also discuss and present some new results on Sylow branching coefficients for symmetric groups.