Convex and Algebraic Geometry

The subjects of convex and algebraic geometry meet primarily in the theory of toric varieties. Toric geometry is the part of algebraic geometry where all maps are given by monomials in suitable coordinates, and all equa- tions are binomial. The combinatorics of the exponents of monomials and binomials is sufficient to embed the geometry of lattice polytopes in algebraic geometry. Recent developments in toric geometry that were discussed during the workshop include applications to mirror symmetry, motivic integration and hypergeometric systems of PDE's, as well as deformations of (unions of) toric varieties and relations to tropical geometry.