Mathematical Sciences: Evolution Equations in Geometry

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The principal investigator will study evolution equations in differential geometry. In particular he will study the Ricci flow and Yamabe flow. Singularities in the solutions of the flow problems will be one of the main focal points of the research. The principal investigator will try to use blow up methods to study these singularities. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.