First presenter Co-presenter(s)
Name :  Jan Verschelde * Name:   
E-mail: E-mail:  
Affiliation: University of Illinois at Chicago Name:   
Department:   E-mail:    
City: Name:   
State/Province:   E-mail:    
Country: USA Name:   
06-08  E-mail:    
Session: 6- Applications of Math Software to Mathematical Research Schedule:
Saturday, 11:30
Related website:  
Title of
Solving Schubert Problems with Littlewood-Richardson Homotopies
Given a sequence of nested linear spaces (called flags) and prescribed dimensions for each flag, a Schubert problem asks for all planes that meet the given flags at the prescribed dimensions. A geometric Littlewood-Richardson rule developed by Ravi Vakil leads to homotopy algorithms to solve a Schubert problem. Littlewood-Richardson homotopies are the families of polynomial systems constructed by these homotopy algorithms. Symbolically, homotopy algorithms degenerate a moving flag, using polynomial equations to keep conditions imposed by other flags fixed. At the degenerate configuration of the flag, a linear system provides a start solution for a path to track by numerical continuation methods. The specialization of a flag follows a combinatorial checker game. For sufficiently generic Schubert problems, the number of paths to track is optimal. The Littlewood-Richardson homotopies are implemented using the path trackers of the software package PHCpack. This is work in progress joint with Frank Sottile and Ravi Vakil.