As a new member of the MAP5, in this occasion I will introduce myself and my past work, along with current interests and future research goals. My work is devoted to macroscale deterministic models of cell population dynamics in cancer and development, with a focus on understanding the mechanisms behind the spatio-temporal sorting of heterogeneous cell populations.

Heterogeneity and plasticity in individual cell behaviour play a fundamental role in developmental and pathological (e.g. cancer) processes. The phenotype of cell, i.e. the ensemble of its observable characteristics determining its behaviour, can be quantified by the level of expression of certain genes or proteins in the cell, which are typically measured on a continuum. For this reason, nonlinear integro-differential equations describing the evolutionary and spatiotemporal dynamics of phenotype-structured cell populations have become increasingly popular in the mathematical community. In particular, in the past 20 years much effort has been put into the analysis of formal asymptotic behaviour in well-mixed and spatially-explicit models, and more recently new interdisciplinary problems emerged in the quest to calibrate these models with experimental data. This talk will provide an overview of the field, covering basics, new trends and open questions on both the mathematical and interdisciplinary fronts.