Colloquia — Fall 2005
Wednesday, November 23, 2005
| Title |
Quasi-stationarity and exit times for a size-dependent branching
process |
| Speaker |
Professor Göran Högnäs
Åbo Akademi University
Finland |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 118 |
| Sponsor |
Professor A. Mukherjea |
Abstract
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.
Tuesday, November 1, 2005
| Title |
Some Problems on the Chromatic Number of Infinite graphs |
| Speaker |
Peter Komjath
Eotovos University
Budapest, Hungary |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 120 |
| Sponsor |
Professor V. Totik |
Abstract
We survey some problems concerning the chromatic number of infinite graphs. A
recent negative solution to Taylor's problems will be sketched.