Besides the traditional directions of topological classification of real algebraic varieties, we mean to focus on enumerative problems and relations to convex geometry via the theory of amoebas and tropical geometry. This will include many recent and notable advances in real algebraic geometry, as well as some of its most important open problems. Of particular emphasis will be the following topics.
- Real algebraic curves. (The pictures below are of two constructions of real plane curves exploiting convexity.)
- Real flexible (J-holomorphic) curves.
- Higher-dimensional real varieties.
- Tropical algebraic geometry.
- Real Solutions to systems of equations. (A survey on geometric aspects of this subject.)
- Algorithms for real algebra via semi-definite programming.
- Real algebraic geometry in applications.
|January 12, 2004 - January 16, 2004||Introductory Workshop in Topological Aspects of Real Algebraic Geometry|
|February 23, 2004 - February 27, 2004||Topology and Geometry of Real Algebraic Varieties|
|April 12, 2004 - April 16, 2004||Algorithmic, Combinatorial and Applicable Real Algebraic Geometry|