Anagrafe della ricerca

Although the research advances, cancer remains one of the most outstanding problems of our society, highlighting a need to develop innovative approaches to the problem that integrate theoretical and experimental strategies. In this context, mathematical models emerge as powerful tools, building a bridge between theory and experiments. The complex nature of tumor phenomena requires new mathematical techniques, and, in turn, the analysis of these new tools requires the development of new mathematics. The novel challenge of IMTIDy is to analyze the interface interactions between tumor and its microenvironment (TME) at two distinct levels: firstly, looking at the effects of tumor-TME interactions on the involved agents; then, deeply studying the cell communication process driving these interactions. The Action is divided into two Work Packages, each focused on one of these levels. WP1) To rigorously model the biomechanical and biochemical interactions at the tumor-TME interface via innovative techniques for the analysis of nonlinear and nonlocal transport models. The model derivation, the analysis of its solutions, their behavior, and stability will contribute to a deeper understanding of the mathematical theory of transport models for tumor dynamics. WP2) To provide a formal description of the microscopic processes leading cell communication via innovative applications of the mean-field theory with singular interaction kernels, and extend it to a multicellular context. This Action represents an interdisciplinary, innovative, and challenging proposal, requiring techniques from PDEs analysis and kinetic theory, complemented by computational and data process skills. It gathers scientists from different communities, gives impulse to existing research lines, and identifies new long-term directions. Combined with the supervisor experience, the excellent training, and the rich host environment, it will enhance the researcher toward an outstanding career in academia.