Applied Mathematics Colloquia by Jose Israel Rodriguez: Curves, Surfaces, and Applied Algebraic Geometry

Speaker: Jose Israel Rodriguez

Title: Curves, Surfaces, and Applied Algebraic Geometry 

Abstract:

Applied Algebraic Geometry (AG) is an inclusive community involving industry, scientists, and mathematicians. It combines centuries worth of AG ideas with modern computing power to drive research into applications from new angles. The success and growth in this area comes from the fact that many problems can be restated in terms of solving systems of polynomial equations. The solution sets to these equations are algebraic sets, also known as algebraic varieties. For instance, algebraic curves like the parabola are one dimensional varieties, while finite sets of points are zero dimensional.

In this talk I will (1) present motivating examples of polynomial systems appearing in applications such as Algebraic Statistics, (2) illustrate the core ideas of methods to describe curves, and if time permits (3) outline a new numerical algorithm (u-generation) for intersecting a curve with a hypersurface for maximum likelihood estimation. No prior background knowledge in algebraic geometry will be assumed.

 

Applied Mathematics Colloquium