Spline Spaces and Subdivision Schemes with Applications in Geometric and Scientific Modeling

The goal of this project is to advance our understanding of the combination of two mathematical tools. The first are multivariate splines, which are used to represent (often complicated) geometric data on a computer. The second are subdivision schemes, wh ich are used for the effective computation of data based on such a representation. Such schemes have for instance been used in the production of animated movies, like Toy Story 2 and Finding Nemo. Possible applications are better methods in geometric mode ling and better numerical schemes for solving differential equations arising in the physical sciences.

The proposed 3-year post doctoral project is for a basic research project in Mathematics, with the goal of advancing our understanding of multivariate spline spaces and subdivision schemes. The project aims to strengthen and build new bridges between seve ral research fields, applying for instance techniques from homological algebra and harmonic analysis to solve problems in spline geometry and subdivision analysis. Possible applications are better methods in geometric modeling and better numerical schemes for solving differential equations arising in the physical sciences.