Description
Many problems in science and engineering can be formulated as computing information about the set of real points satisfying polynomial equations and inequalities. Some examples include synthesizing a linkage in kinematics, computing and analyzing the steady-state solutions to a polynomial dynamical system, and reconstructing a scene in computer vision. Since different problems could require a different amount of information about the real solution set, this talk will summarize four computations in real numerical algebraic geometry: 1) existence of a real solution, 2) smooth points and dimension of the real solution set, 3) decomposition into smoothly connected components, and 4) cell decomposition for a complete description of the real solution set. Each computation will be illustrated with an example along with a discussion about benefits and potential drawbacks. This talk covers computational methods created jointly with a variety of collaborators including Silviana Amethyst, Dan Bates, Gian Mario Besana, Joe Cummings, Sandra Di Rocco, Wenrui Hao, Hoon Hoon, Katherine Harris, Cliff Smyth, Andrew Sommese, Agnes Szanto, and Charles Wampler.
