Speaker
Description
In this talk, I will describe my group's ongoing research into designing mathematical models that can learn from different data modalities simultaneously: such as clinical reports, whole-genome sequencing, and medical images. We apply these to describe risk stratification, patient outcomes, and subclonal evolution for several different pre-cancerous conditions. In my lab, we draw from both stochastic processes, especially compound birth-death processes, and differential equations and dynamical systems, especially hyperbolic PDEs. We recently succeeded in developing a numerical integration scheme for directly computing survival probabilities of a first-order birth-death process on an arbitrary directed graph, without the use of stochastic simulations: ten million times faster than the state of the art. I will explain how this has let us study the genomics and growth of vestibular schwannoma, a type of of slow-growing brain tumour, in unprecedented detail, and how our research is informing real treatment decisions.
Although I work primarily on applications, I am also interested in "theory". All the models we have studied have shown emergent wave-like behaviour, even models without any obvious spatial dependence: I will try to explain why this happens, and point out questions for future research, both theoretical and applied and in nature.
