Short Talk: Caelan Atamanchuk

 A \emph{temporal graph} is a pair $(G,\lambda)$, where $G$ is a simple graph and $\lambda$ is some ordering of the edges of $G$. We say that a path $P$ from $u$ to $v$ in $G$ is \emph{increasing} if $\lambda$ increases when travelling from $u$ to $v$ on $P$, and we say that $u$ \emph{can reach} $v$ if there is an increasing path from $u$ to $v$ in $G$. In recent years, a lot of study has been put towards understanding how reachability in temporal graphs compares to reachability ordinary static graphs. The case where $G$ is an Erd\"os-R\'{e}nyi random graph and $\lambda$ is a uniform permutation (called a \emph{random simple temporal graph}) has been one model of large interest, and many nice phase transitions for varying levels of temporal connectedness have been identified. Using the study of random simple temporal graphs as motivation, I will introduce the notion of random temporal trees and present some of their interesting properties. The results will come from joint work with Luc Devroye and Gabor Lugosi.