Applied Probability and Statistics

Our research is centered on mathematical problems  arising in   statistics and  in systems biology. We are  interested in robust covariance matrix estimation using data from Grassmann manifolds.  Such models appear in many applied contexts  of interest like image and video analysis, and offer a very interesting framework where mathematical techniques from differential geometry and probability can be developed. We also focus on computation in natural systems, and try  to understand how living systems perform statistical inference.

   

Mathematical Biology

Mathematical modelling is becoming more and more instrumental in life sciences; the data complexity and the high number of interacting components, from molecules to animals, render intuitive reasoning very difficult. The idea consists in formulating mathematically how certain biological units affect each other and how these interactions affect the whole system. We study phyllotaxis by trying, for example, to explain the formation of geometrically regular patterns in plants like spirals in sunflowers. We also focus on the structural stability of complex ecosystems; in this setting, we try to understand how the topologies of complex biological networks affect persistence and biodiversity. I work on these topics with my PhD students  Linard Hoessly, Lucia de Andres and Xavier Richard.

   

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