Abstract for the talk on 09.11.2017 (14:00 h)Seminar on Nonlinear Algebra
Jose Israel Rodriguez (University of Chicago)
Trace Tests in Numerical Algebraic Geometry
Numerical algebraic geometry uses numerical algorithms to study algebraic varieties, which are sets defined by polynomial equations.
It is becoming a core tool in applications of algebraic geometry outside of mathematics. Its fundamental concept is a witness set which gives a representation of a variety that may be manipulated on a computer. A trace test is used to verify that a witness set is complete and provide stopping criteria for algorithms. Recently, there have been further developments in computational algebraic geometry to study varieties in a product space, which is the natural setting for solutions of parameterized polynomial systems. In this talk, we discuss some of these developments and a new trace test for these varieties. We demonstrate the methods' effectiveness in examples from various areas of science and statistics.