Workshop

The topological study of real algebraic varieties originated in the 19th century -- it was featured in Hilbert's 16th problem on the classification of real algebraic plane curves. This subject has recently grown in many directions, including higher dimensional real varieties, amoebas and tropical algebraic geometry, J-holomorphic curves from symplectic geometry, and enumerative real algebraic geometry. Some of these developments have led to advances important to applications and to the problem of real solutions to polynomial equations, including algorithms. This introductory workshop will feature survey lectures intended to introduce these topics and convey their interdependence to the mathematical public. This program will include the following talks. Oleg Viro: Topology of real algebraic curves Grisha Mikhalkin and Bernd Sturmfels: Tropical algebraic geometry and amoebas. Frank Sottile: Enumerative problems and real solutions to equations. Lalo Gonzalez-Vega: Real algebraic geometry in industry