SIAM’s final conference in the year of “Mathematics of Planet Earth” covers the analysis of partial differential equations. This topic relates to developing methods to analyze the equations which result, in many cases, from modeling physical or biological phenomena. While the focus is on the mathematical analysis rather than the physical models, one nevertheless can readily see the contacts to mathematics of planet earth and the power of mathematics to understand world around us.

To cite one example, the conference offers an invited presentation by Philip Maini on “Modelling Collective Cell Motion in Biology.” The talk will consider three different examples of collective cell movement each of which requires different modeling approaches. One involves the movement of cells in epithelial sheets. Another is cranial neural crest cell migration which requires different kind of model. The third is acid-mediated cancer cell invasion, modeled via a coupled system of nonlinear partial differential equations. These can all be expressed using a common framework (nonlinear diffusion equations), which then can be used to understand a range of biological phenomena.

Such is the power of mathematics to develop tools which apply across a wide range of phenomena.