Numerical Homotopy Algorithms for Enumerative Geometry

Abstract:

In a 1998 paper on Numerical Schubert Calculus, Birk Huber, Frank Sottile, and Bernd Sturmfels proposed numerical Pieri homotopy algorithms to solve problems in enumerative geometry. Implementations of these algorithms ran on specific examples of intersection problems whose solution set is entirely real. Jointly with Yusong Wang, the Pieri homotopies were applied to the output pole placement problem in linear systems control. Following a geometric proof of the Littlewood-Richardson rule, Frank Sottile and Ravi Vakil designed deformation methods to solve general Schubert problems. Current work is directed to implement these new Littlewood-Richardson homotopies.

Schubert Calculus and Schubert Geometry, Banff International Research Station, 18-23 March 2007.

slides of the talk