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Numerical Algebraic
Geometry Andrew Sommese: Director, Center for Applied Mathematics and Duncan Professor of Mathematics, Notre Dame University 11:00 AM Tuesday 24 July 2007, Middlesex College Room 108 (Joint Applied Mathematics and Mathematics Seminar) Following an overview of Numerical Algebraic Geometry, some recent ongoing work will be presented: a) Some of the numerical issues dealt in the design of software for Numerical Algebraic Geometry and some details about Bertini, the software package recently released by D. Bates, J. Hauenstein, C. Wampler, and myself. b) work with C. Wampler on numerical computation of exceptional sets of algebraic maps (with regards to fiber dimension) by means of iterated fiber products. c) work with D. Bates, C. Peterson, and C. Wampler on numerical computation of the geometric genus of curve components of algebraic sets. |
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Geometric Symbolic-Numeric Methods for
Differential and Algebraic Systems Wenyuan Wu: The University of Western Ontario 2:00 PM Tuesday 24 July 2007, Middlesex College Room 204 (PhD Public Lecture) General systems of PDE arise frequently in diverse applications. Existing approaches can be prohibitively expensive and are numerically unstable for approximate systems. In this talk, I will introduce new practical and stable methods for such systems by using symbolic-numeric computation techniques. These methods and their mathematical theory for general PDE lead to a new area called Numerical Jet Geometry. I will also discuss some open problems in this new area. |