University of South Florida
College of Arts and Sciences
Title: Quasi-stationarity and exit times for a size-dependent branching process
Speaker: Göran Högnäs, Åbo Akademi University
Place: PHY 118
A size-dependent branching model of the evolution of a single species population is introduced. The short-term behavior mimics the corresponding deterministic dynamical system very closely, but the branching model hits \(0\) eventually, i.e., the population goes extinct in contrast with the deterministic model which remains positive at all times. It turns out that the so-called quasi-stationary distribution (q.s.d.) of the branching model gives the right asymptotics. The q.s.d. approximates the attracting limit cycles of the deterministic system. I will also discuss some results, mainly due to Klebaner and Liptser, on the order of magnitude of the extinction times.
Title: Some Problems on the Chromatic Number of Infinite graphs
Speaker: Peter Komjath, Eotovos University
Place: PHY 120
We survey some problems concerning the chromatic number of infinite graphs. A recent negative solution to Taylor's problems will be sketched.