Colloquia
Dan Bates
CAM COLLOQUIUM
“Bounding and Finding the Real Solutions of Fewnomial Systems”
Dan Bates
Institute for Mathematics and its Applications
University of Minnesota
Monday March 10, 2008
4:00PM in 127 Hayes-Healy Center
*TEA – 3:30PM in Math Lounge – 257 Hayes-Healy*
Homotopy continuation is a powerful took for computing approximations for all isolated solutions of polynomial systems. One drawback to this technique is that it finds all complex solutions, even if only the real solutions are of interest. In recent years, there has been significant progress by people such as Bernstein, Kouchnirenko and Khovanskii in finding an upper bound for the number of real solutions, particularly in joint work with F. Bihan (Savoie) and F. Sottile (Texas A&M). The theory behind this bound (Gale duality), together with the Khovanskii-Rolle theorem, lays the groundwork for a new numerical method to actually compute all real solutions of fewnomial systems, at least in certain cases. This method is joint work with F. Sottile and will also be described in some detail.
