CONFERENCE: Tutorials in Applicable Algebraic Geometry

Colorado State University, Fort Collins CO

Investigators

Abstract

There has recently been a significant increase in the application of the methods of algebraic geometry to problems outside of mathematics. The resulting interdisciplinary work necessarily entails much interaction between experts in algebraic geometry and those from other disciplines. The PI will run a workshop July 29-31, 2013 focused on introducing non-experts to two fundamental tools rooted in algebraic geometry: numerical algebraic geometry and toric geometry. Authors of recent books in these two areas will give lectures: Frank Sottile and Jonathan Hauenstein for numerical algebraic geometry, John Little and Hal Schenck for toric geometry. These lectures will serve as a rapid introduction to the methods and software from these two areas, focused on the value for problems coming from applications. This meeting will take place at the Pingree Park mountain campus of Colorado State University. Mathematical problems in application areas can sometimes be converted into a certain type of problem, the polynomial system. For years, there was no efficient way to solve polynomial systems, so researchers had to find different, sometimes less desirable, formulations for their problems. However, with recent developments in numerical algebraic geometry and toric geometry, it is now reasonable to solve relatively large polynomial systems directly. These new computational tools open the door to study problems that were previously too difficult to consider. For example, in kinematics, the introduction of numerical algebraic geometry has already resulted in the ability to solve long-standing problems and to discover new mechanisms with special properties. The workshop supported by this award will help to expedite the use of these powerful new tools by the researchers who need them.