Mathematical Challenges in Modelling Cancer Dynamics

Cancer is a complex disease, whose high incidence and diversity constantly increase the demand to better understand it. Mathematical models are being increasingly used to complement experimental research, thanks to the flexibility of modelling frameworks, the systematic understanding provided by analytical investigations, the reproducibility of numerical simulations, and the possibility to integrate empirical data. Conversely, modelling tumour dynamics is one of the most prolific sources of new remarkably challenging mathematical questions. This workshop will bring together young researchers and established mathematicians specialised in the modelling of cancer dynamics. The aim is to showcase recent progress and discuss new open problems in the field, concerning: (i) modelling of tumor dynamics (growth, metastasis, treatment, etc); (ii) analysis of qualitative properties and asymptotic behaviour of kinetic and PDE models (e.g. hard congestion, surface tension, phenotypic heterogeneity); (iii) numerical simulation of these models (e.g. conservative schemes, capturing singularities); (iv) data integration (e.g. image processing, statistical methods, artificial intelligence).