Research

Concentration dynamics in PDE models of adaptive dynamics

My doctoral thesis focuses on the dynamics of Dirac mass concentrations in non-local partial differential equations motivated by ecology and evolutionary biology. It aims to describe selection phenomena among phenotypically structured populations. Starting with the basic principles of the Darwinian theory of evolution, heredity, variability and adaptation, I studied equations on population distribution on a continuous trait space which combine trait-dependent demographic coefficients and non-local terms that stand for ecological interactions. These equations feature non-linear and non-local terms, and a small parameter that introduces the ecological and evolutionary time-scales. Using appropriate assumptions, inspired from adaptive dynamics theory, the aim is to prove that the asymptotic solutions to these equations concentrate in Dirac masses located on the dominant traits.

Data-driven modeling of metastatic development in kidney cancer

Renal Cell Carcinoma (RCC) is the most common type of kidney cancer in adults and, when it has spread to other organs to form metastases, five year survival is less than 10%. Standard therapies, including chemotherapeutic drugs, are rarely curative and drug resistance eventually occurs. The pathophysiology of RCC still remains poorly understood, and there is a clear need to identify key mechanisms in the disease progression in order to investigate new therapeutic ways. The goal is to build a systems biology model, integrating multi-scale data (transciptomic, methylomic, physiological and MRI data), which will allow to describe the dynamics of tumor and metastatic progression, and enable to identify its crucial processes.