At this colloquium, we are happy to welcome:

Franz Baumdicker (Universität Tübingen)

Learning from Trees in Population Genetics

Modern genomics offers meanwhile an unprecedented detailed view into the diversity and evolution of biological populations. However, insights from huge biobanks also challenge classical population genetic models that describe evolutionary processes, such as mutation, selection, and recombination and how these processes shape genetic variation.
I will present recent developments at the interface of mathematical population genetics, simulation-based inference, and machine learning, with a particular focus on bacterial evolution. For example, results from coalescent theory can be integrated with neural networks that estimate population genetic parameters. However, applying machine learning in this context is far from straightforward as population genetic data reflect complex genealogical histories. Recently developed effective simulation tools based on the ancestral recombination graph, which offers a compact and informative representation of the evolutionary history, are crucial for the recent advances in data-driven population genetics and hold particular promise for a better understanding of bacterial evolution, human health, and beyond.

André H. Erhardt

Mathematical modeling and analysis of cardiac dynamics

Mathematics for healthcare and quantitative biomedicine have become increasingly important, and include various aspects such as modeling and simulation. Important biomedical applications include tumor growth, electrophysiology, tissue regeneration, and biomedical engineering. In this line, the mathematical modeling of cardiac single cells by a set of nonlinear differential equations including multiple time scales is presented, as well as the mathematical description of the heart. Moreover, the analysis of complex cardiac dynamics by means of bifurcation theory is demonstrated. One specific focus will be on the ion current interaction leading to so–called early afterdepolarizations, which are pathological voltage oscillations during the repolarization or plateau phase of cardiac action potentials caused by ion channel diseases, drugs or oxidative stress and are considered as potential precursors of cardiac arrhythmia. Finally, synchronization effects on tissue level, e.g. the occurrence of spiral waves, using FEniCS (a Python-based open-source finite element library) are discussed.