Abstract: Let p be a prime, let G be a finite group and let P be a Sylow p-subgroup of G.
Over the last couple of years I have been interested in studying the structure of the
restriction to P of any irreducible character of G. More precisely, if χ ∈ Irr(G) then
the restriction χ P decomposes into the sum of irreducible characters of P appearing
with integer multipicities. These multiplicities are called Sylow Branching Coefficients
(SBCs). In this talk I will present some new results concerning SBCs in the case where
G is the symmetric group. Moreover, I will mention how the study of this topic allowed
us to prove a Conjecture formulated by Malle and Navarro in 2012.
This talk is based on joint works with Stacey Law, Jason Long, Carolina Vallejo
and Giada Volpato.