The last two decades have witnessed the "coming of age" of mathematical oncology as a discipline, and it has now firmly taken center stage as one of the major themes of modern applied mathematics. Research efforts in cancer modeling have resulted in models that, on the one hand, can represent all the key stages of solid tumor growth from avascular growth, to tumor-induced angiogenesis and vascular growth. On the other hand, in other directions, researchers have started to model the immune response to cancer, as well as the processes of invasion and metastasis. New areas of investigation have also focused on the spatiotemporal modeling of intracellular pathways associated with cancer and how these can be linked through multi-scale modeling to tissue level manifestations of malignant tumors. Yet other investigations relate directly to the delivery of anti-cancer drugs to malignant tumors, including their interstitial transport and cellular uptake, which is a complex process involving various biochemical, mechanical, and biophysical factors. 

Mathematical modeling provides a means through which to probe and understand this complexity better, as well as providing a means to examine interactions between contributing components in a systematic way (through the use of "in silico" experiments via computational simulations, and mathematical analysis). In principle, new disciplines and approaches may lead to breakthroughs and exciting discoveries in traditional fields such as oncology. However, to be useful, the new approaches should be coupled with experimental investigations and clinical practice, and should be integrated into the existing body of knowledge and wisdom accumulated in oncology. In the past decade, several interesting and unexpected ideas have arisen, as a result of interdisciplinary interactions between researchers from very different backgrounds - these include statistics, material science, fluid mechanics, population dynamics, and evolutionary game theory amongst many others. 

It seems clear that progress in this field, so interdisciplinary in nature, will depend critically on the ability of team members to speak a common language. By this, we do not mean that the mathematician/physicist must become an expert in cancer biology/clinical oncology, or vice versa that the cancer biologist/clinical oncologist must understand the theory of partial differential equations or the fundamentals of physics; but there must be a common appreciation of what a mathematical model is, what features and mechanisms it purportedly captures, what conclusions can be reasonably drawn from such a model and what it's shortcomings might be. There needs to be a spirit of mutual understanding and appreciation amongst teams composed of experimental, clinical and theoretical scientists, and an open forum for alternative (sometimes contrarian) views and stimulating new ideas. We (biologists, clinicians, physicists, mathematicians..) all think very differently and therein may lie the secret to unlocking the mysteries and challenges posed by cancer since time immemorial.

This workshop will bring together a balanced international group of both mathematical and experimental/clinical scientists working at the forefront of the interdisciplinary field of mathematical oncology. The topics covered will span a broad spectrum of problems of current interest in oncology and will hopefully stimulate further research in new and novel directions. This workshop is part of the 10-year anniversary celebration of the establishment of the CMM at the Fields Institute. It will feature a number of invited talks as well selected contributed.