• Stochastic modelling in the life science: From evolution to medicine
• Trimester Seminar Series

• Summer School: Stochastic Modelling in the life sciences (May 9-13 2022)
• Workshop: Impacts of dormancy and latency on host parasite dynamics (May 16-20, 2022)
• Workshop: Population Genetics, Interacting Particle Systems and Stochastic Flows: a duality perspective (June 20-24, 2022)
• Workshop: Interacting Particle Systems in Mathematical Biology (July, 25-28 2022)
• Hausdorff School: “Inverse problems for multi-scale models”
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Trimester Seminar Series

Speaker: Arno Siri-Jégousse

Title: Exchangeable coalescents, theory and applications

Abstract:

In this series of talks, I will show pieces of the coalescence theory: Poisson construction, exchangeability, random partitions. After this introduction to basic concepts, I will expose some applications to population genetics.

Estimation of the coalescent measure. Coalescents are used to model genealogies of populations and the shape of these trees can be inferred thanks to genetic data of a present population. I will provide a non-parametric method to estimate the characteristic measure of coalescence and a recipe to apply this method with real data.

Asymptotics of Dirichlet-type coalescents: This class of processes can be used to model genealogies of populations suffering bottlenecks during their evolution. They also provide an example for exchangeable cpañescents with multiple and simultaneous collisions. Finally this class has a nice connections with urns and their asymptotics can be studied using Stein's method for urn models.