Title: Why Polyhedra Matter in Nonlinear Equation Solving Date/Time: Monday, October 24, 2005, 9:30-10:30 am Location: Building 980, Room 95 (Sandia NM) Brief Abstract: Polyhedra are fundamental in linear optimization and their importance in nonlinear optimization is now being recognized in many ways. In this talk, we introduce some of the most useful connections between polyhedra and polynomials. We start by showing how the number of complex solutions of any system of polynomial equations can be expressed in terms of volumes of polytopes. Integer linear equations also enter in an important way. Time permitting, we will discuss some recent algorithmic speed-up techniques for solving nonlinear equations, including polyhedral homotopy and tropical geometry. We will also touch upon the subtleties behind counting just the real solutions of a nonlinear system. CSRI POC: Mark (Danny) Rintoul, (505) 844-9592 |