Phase-field modeling allows to effectively capture the evolution of interface phenomena by means of a diffuse interface approximation, leading to highly nonlinear partial differential equations. These models have found plenty of applications since their first introduction almost one hundred years ago. More recently, they have been shown to be very well suited for the modeling of Cell Biology phenomena, including tumor and tissue growth. In particular, recall that tumors are nowadays a very hot topic, since they are one of the major causes of death worldwide, and the understanding of their behavior is a prominent challenge of modern scientific research. Considerable progress has been made, with more and more efficient therapies, but  interdisciplinary collaborations are imperative to grasp more insights on cancer evolution. Multiscale mathematical models, especially through phase-field modeling, provide an essential quantitative tool that could be of help in diagnostic and prognostic applications. Additionally, phase-field models have nowadays found relevant applications in the study of tissue growth, cell migration, and Liquid-Liquid Phase Separation processes. These models can be either local or nonlocal, in accordance to the fact that in many  biological phenomena, like cell-cell adhesion, the use of nonlocal nonlinear aggregation-diffusion equations is an essential tool. On the other hand, a modeling approach alternative to phase-field is the use of free boundary problems, to explicitly track the phase interfaces. This has attracted the interest of mathematicians in recent years for their applications in biomedical modeling.
 
Since all these modeling approaches are intuitively connected to each other, one of the most challenging goals of Mathematics  is not only the understanding  of quantitative, qualitative, and asymptotic properties of the solutions to the corresponding equations, but also the analysis of their deep connections through, for instance, singular limits. The complexity  of such topics asks for a wide variety of advanced mathematical techniques, bridging functional analysis to geometric measure theory, monotone and convex analysis to optimization theory and numerics. Such variety  attracts researchers from a range of areas of expertise. 

The great relevance of biological applications and the outstanding diversity of theoretical tools involved have contributed to an amazing development of this field in the last years. However,  several aspects are still widely open in many directions. One of the main objectives of this workshop is to bring together, from all over the world, researchers  interested in the  modeling and mathematical analysis of biological systems, in order to tackle the most  challenging and recent advances of the theory, possibly creating an international environment for growing new seminal ideas.