Abstract or Additional Information
Galton-Watson processes were introduced by Sir Francis Galton and Reverend Henry William Watson in the mid 1870s as a method of investigating the extinction probabilities of family names. In the 1.4 centuries since, mathematicians and others have applied Galton Watson theory to study Y-chromosome transmission in genetics, the propagation of cancer cells, and the spread of AIDS, to name a few examples. In this talk, I will formulate and discuss the mathematics behind the classic Galton-Watson model and derive the probability that a surname goes extinct (or equivalently and more happily, survives). I will then present recent results on an application of Galton-Watson theory to the study of disease transmission in a well mixed human population. This talk should be accessible to anyone who has passed calculus I and has seen power series.