Exploring the Potential Energy Landscape Over a Large Parameter-Space

Understand

Solving large polynomial systems with coefficient parameters are ubiquitous and constitute an important class of problems.

• We demonstrate the computational power of two methods--a symbolic one called the Comprehensive Gr\"obner basis and a numerical one called the cheater's homotopy-applied to studying both potential energy landscapes and a variety of questions arising from geometry and phenomenology.
• Particular attention is paid to an example in flux compactification where important physical quantities such as the gravitino and moduli masses and the string coupling can be efficiently extracted.