Position:
Assistant Professor of Mathematical Sciences
Education:
PhD, Applied Mathematics, University of Colorado, 2001
MS, Applied Mathematics, University of Colorado, 1996
AB, Mathematics, Princeton University, 1994
Professional Interests:
In general, my interests include numerical analysis, applied analysis, and mathematical biology. In particular, I have recently developed and analyzed a truly meshfree first-order system least-squares method for partial differential equations that employs a partition of unity. Avoiding proper tessellation may be preferable in applications where nodes, or subsets of nodes, either move or vanish. Biological modeling of cell population scale dynamics, centered about intracellular models of gene product interactions, provide an example where simple coverings in lieu of proper tessellations provide a more natural discretization. Specifically, my group is engaged in modeling that explores the influence of physiological levels of DNA damage, and thus cellular response to this damage, on the timing and distribution of neural progenitor cell fate decisions during cortical development. Importantly, this model allows us to test hypotheses about not only the nature of these cellular decisions but also the generation of genetic diversity among the neurons that comprise cerebral cortex. This work is in collaboration with M.J. McConnell of BioX, Stanford University. Linking these two strands of research and developing spatially-informed models of proliferative populations of neural progenitor cells is a long-term aspiration.
Selected Publications:
Related Web Sites:
Personal home page.
Department of Mathematical Sciences.
Last Updated: 2007/05/02