Convex and Algebraic Geometry

Angular Momentum, Convex Polyhedra and Algebraic Geometry

The three families of classical groups of linear transformations (complex, orthogonal, symplectic) give rise to the three great branches of differential geometry (complex analytic, Riemannian and symplectic). Complex analytic geometry derives most of its interest from complex algebraic geometry, while symplectic geometry provides the general framework for Hamiltonian mechanics. These three clas...

Non-Convex Optimization via Real Algebraic Geometry

The high level purpose of this paper is to describe some recent advances in the field of Mathematics called Real Algebraic Geometry, and discuss some of its applications to complexity theory, and non-convex optimization. In particular, one of the questions underlying the entire development, is the crucial question: What makes an optimization problem difficult or easy? Along the way, we try to p...

Real Algebraic Geometry in Convex Optimization

Real Algebraic Geometry in Convex Optimization

Applications of Convex and Algebraic Geometry to Graphs and Polytopes

Applications of Convex and Algebraic Geometry to Graphs