Ian Seong (University of Wisconsin–Madison)「On the recovery of the underlying projective geometry from a given Grassmann graph」
This talk is about a type of distance-regular graph called a Grassmann graph. A Grassmann graph $\Gamma$ is defined using a projective geometry. Our motivation is to recover the projective geometry from $\Gamma$. With this motivation in mind, we present numerous results that describe how the projective geometry is related to $\Gamma$. These results concern the following situation. Pick distinct vertices $x,y$ of $\Gamma$ that are not adjacent and at distance less than the diameter of $\Gamma$. We investigate the five orbits of the stabilizer $Stab(x,y)$ in the local graph $\Gamma(x)$.