The sequencing of the human genome and the development of new methods for acquiring biological data have changed the face of biomedical research. The use of mathematical and computational approaches is taking advantage of the availability of these data to develop new methods with the promise of improved understanding and treatment of disease.

I will describe some of these approaches as well as our recent work on a Bayesian method for integrating high-level clinical and genomic features to stratify pediatric brain tumor patients into groups with high and low risk of relapse after treatment. The approach provides a more comprehensive, accurate, and biologically interpretable model than the currently used clinical schema, and highlights possible future drug targets.

Grothendieck Hilbert and Quot schemes give a powerful tool in studying parameter spaces in algebraic geometry. We are planning to give an overview of basic results related to them.

A multispecies continuum model is developed to simulate the dynamics of cell lineages in solid tumors. The model accounts for spatiotemporally varying cell proliferation and death mediated by the heterogeneous distribution of oxygen and soluble chemical factors. Together, these regulate the rates of self-renewal and differentiation of the different cells within the lineages. As demonstrated in the talk, the feedback processes are found to play a critical role in tumor progression and the development of morphological instability.

*Pizza and soda will be served!