US-France (INRIA) Cooperative Research: Symbolic and Numerical Methods for Geometric Modeling

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0421771GoldmanThis three-year U.S.-France cooperative research project addresses solutions for polynomial equations systems and applications to problems in geometric modeling and molecular biology. Ronald Goldman of Rice University and the GALAAD group at the French National Institute for Research in Informatics and Applied Mathematics (INRIA), led by Bernard Mourrain, will develop techniques in algebraic computation. The GALAAD team will concentrate on polynomial equations and applications to computational biology. This is complemented by Rice University's focus on polynomial equations and their applications to computational geometric modeling.Intellectual Merit: Many applications in geometric modeling and computational biology require fast robust methods for solving systems of polynomial equations. The investigators propose two approaches to solving systems of polynomial equations: innovative resultant techniques and numerical methods based on Bezier subdivision. They will also implement their algorithms in the C++ library SYNAPS.Broader Impact: The proposed methods will be applied to problems in geometric modeling and computational biology. To aid in geometric modeling, they will investigate some approaches to computer representations of shape and apply their techniques to more efficient solutions to standard problems representing rational curves and surfaces. In computational biology they will try to recover the three-dimensional structure of a molecule from partial information generated by NMR experiments. The results may be useful for automated drug design, protein folding and studies of cell properties. The project also gives a U.S. graduate student training in an international environment via research immersion with the INRIA group and provides an opportunity to develop connections for future international collaboration.