Kisun Lee, Introduction to Numerical Algebraic Geometry

Numerical algebraic geometry employs numerical techniques for problems in algebraic geometry. This talk begins with a question reminding the meaning of solving a (polynomial) equation. It overviews the homotopy continuation as a method for finding solutions to a system of polynomial equations. After problems from algorithmic and application points of view in numerical nonlinear algebra are introduced, we discuss how the results from numerical techniques can be certified. No pre-knowledge from graduate-level algebraic geometry is assumed.