Date and place: November 20, 2014. 16:00. CRM, POL1.
Speaker : Matthew Gelvin
Title: Minimal characteristic bisets for saturated fusion system
Abstract: A \emph{characteristic biset} for the fusion system $\mathcal{F}$ on the $p$group $S$ is a finite set $\Omega$ with commuting left and right $S$actions. $\Omega$ must satisfy certain properties that mimic the left and right multiplications of $S$ on a finite Sylow supergroup inducing $\mathcal{F}$.
The parameterization of $\mathcal{F}$sets implies the existence of a unique minimal characteristic biset $\Omega_{\mathcal{F}}$, which should be thought of as \emph{the} minimal characteristic biset for $\mathcal{F}$. In this talk, I will defend this claim by discussing the close connections between $\Omega_{\mathcal{F}}$ and other central notions in $p$local finite group theory, including $p$constraint, centric linking systems, and $K$normalizers.
Date and place: November 21, 2014. 12:00. CRM, A1.
Speaker : Alex González (Kansas State University)
Title: Irreducible components of plocal compact groups
Abstract: Irreducibility was introduced in earlier work as a criterion to classify all plocal compact groups of rank 1, and could be thought of as an algebraic analog of connectivity. A plocal compact group is said to be irreducible if its underlying fusion system contains no proper normal subsystems of maximal rank. In this talk I will sketch how to show that every plocal compact group has a unique irreducible component, by using group theoretical techniques of Chermak.
