New Directions in Computational Algebraic Geometry

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

This project develops new algorithms and new applications for computational algebraic geometry. If focusses on the following four specific topics: Computing amoebas, toric algebra of graphical models, semi-definite programming and the real Nullstellensatz. It involves tools from combinatorics, commutative algebra and symbolic computation, specifically the method of Grobner bases. The investigator also writes two books, one on Solving Systems of Polynomial Equations, and the other on Combinatorial Commutative Algebra. This project develops new algorithms and new applications for computational algebra. The research in this project is partly collaborative with researchers in other fields, and it has applications to Statistics, Bioinformatics and Computer Science. The use of algebraic methods plays an increasingly important role for the analysis of the U.S. census data provided by the National Institute for Statistical Sciences, and this project provides foundational research for this application. In Computer Science, these techniques are used in machine learning and artificial intelligence.