The ultrafilter theorem in real algebraic geometry

Numerical Real Algebraic Geometry

Sottile’s lectures from the Oberwolfach Seminar “New trends in algorithms for real algebraic geometry”, November 23–28, 2009.

Enumerative Real Algebraic Geometry

Two well-defined classes of structured polynomial systems have been studied from this point of view—sparse systems, where the structure is encoded by the monomials in the polynomials fi—and geometric systems, where the structure comes from geometry. This second class consists of polynomial formulations of enumerative geometric problems, and in this case Question 1.1 is the motivating question o...

Topology and Real Algebraic Geometry

The problem of solving real polynomial equations long fascinated people. Starting with a finite number of points on the real line one can get many complicated spaces as zero sets of polynomials. For example every closed P.L. manifold occurs as an algebraic set [3]. The main goal of understanding the topology of algebraic sets is to topologically characterize the image of the forgetful functor {...

Computational Real Algebraic Geometry 3 THE DECISION

Real Algebraic Geometry in Convex Optimization

Real Algebraic Geometry in Convex Optimization