Back to Departmental Colloquium: Fall 2008
Departmental Colloquium
Date: Thursday, Nov 20, 2008
Time: 4:15PM
Location: JWB 335
J. Maurice Rojas
Texs A & M
Title |
ABCs of Real Algorithmic Geometry |
Abstract |
We survey recent advances toward basic algorithmic questions in real algebraic geometry. In particular, we consider the two questions and their algorithmic complexity: (1) Does a system of sparse polynomial equations have a real root? (2) What is the topology of a real algebraic set defined by a set of sparse polynomial equations? A special case of Question (2) is counting real roots, and even here optimal upper bounds are still an open question. So we also review some concrete examples. Along the way, we will see an unusual connection to the famous Masser-Oesterle ABC-Conjecture, and an extension of Smale’s 17th Problem (on approximating complex roots of polynomial systems). We assume no background in complexity theory or algebraic geometry. |
Algebraic Geometry
Topology
Geometry and Topology