Course Description:

Branching Process has been widely used as a mathematical model to describe the reproductive dynamics in various areas such as the extinction of surnames in genealogy, the spread of disease in epidemiology and ecology, the mutation of cancel cells in medicine, the propagation of neutrons in a nuclear reactor as well as the stock prices in mathematical finance. The purpose of this short course is to provide a rough view of the theory of branching processes, the coalescence problem and their applications. 

 

In the first Lecture, Dr. Athreya will start the course with the single type discrete time Bienaymé-Galton-Watson (BGW) branching process, the martingale property for the finite mean case and the Kesten Stigum LlogL theorem. Then introduce the multi-type BGW process, the Perron-Frobenius theorem for nonnegative finite irreducible matrices, application to finite type BGW processes and some limit theorems.

 

In the second lecture, he will introduce the embedding of BGW processes in Polya urn schemes and the growth of preferential attachment random graphs via continuous time branching processes.

 

In the third lecture, Dr. Athreya will talk about the infinite mean case of BGW process, the coalescence problem and some open problems related to branching processes.