Advanced topics in applied probability
Time and place: Tuesdays and Thursdays, 10-12, Room 1.008
In this lecture we will introduce and discuss what has become known as "stochastic individual based models of adaptive dynamics". Mathematically, these are measure valued continuous time Markov processes that describe the dynamics of populations of individuals that are subject to the evolutionary mechanisms of birth, death, mutation and competition/interaction. They have been introduced to furnish simple mathematical models that allow to derive basic ferature of the biological theory of adaptive dynamics. This will mainly involve the derivation of scaling limits with respect to population size, mutation rates, and mutations step size.
I will write lecture notes as we go.
1) Ethier, Stewart N.; Kurtz, Thomas G. Markov processes. Characterization and convergence. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York,
2) Bansaye, Vincent; Méléard, Sylvie Stochastic models for structured populations. Scaling limits and long time behavior. Mathematical Biosciences Institute Lecture Series. Stochastics in Biological Systems, 1.4. Springer, Cham;
3)Dawson, Donald. Introductory Lectures on Stochastic Population Systems. 2017.
For a popularised historical survey, the following is great reading:
4) Mukherjee, Siddartha. The Gene. Bodley, 2016.
Requirements: Good knowledge of probability theory on the level of Stochastic Processes or better Markov processes
Complementary lecture series "What medicine wants from mathematics"
A series of talks from members of the faculty of medecine will take place on Thursdays, 9h s.t. before the main lecture. The idee is to get an impression of what questions people form the life sciences have where they may expect help from mathematicians, The series will begin on April 18 in Room 1.008 with a talk by Prof. Dr. Michael Hölzel. Here is the full schedule of talks.