The focus of this workshop is the computational study of enumerative problems. Classically, an enumerative problem asks how many geometric objects have a prescribed position with respect to other fixed geometric objects. Famous examples include:

• How many lines go through four lines in $\mathbb{C}^{3}$?
• How many lines are contained in a cubic surface in $\mathbb{C}^{3}$?
• How many conics are tangent to five conics in the plane?

(The answers to these questions are 2, 27, and 3264, respectively)

A modern definition of an enumerative problem may be any problem, expressible by polynomial equations in variables and parameters, that has finitely many solutions given fixed generic parameters. Such problems are widespread in applied sciences like computer vision, statistics, and physics for example.

Given an enumerative problem, counting its solutions is the tip of the iceberg. Beyond enumeration lies questions about symmetries, solvability, real behaviour, and computation. Techniques from a broad range of disciplines lend themselves to the creation of algorithms and software designed to answer these questions. "Computational Enumerative Geometry" refers to this approach of using computers to solve, experiment with, and prove theorems about,  enumerative problems. 

This workshop features leading experts in several areas of research which support computational enumerative geometry. The days are thus themed:

Day 1 - Enumerative Geometry and Combinatorics

Day 2 - Computational Algebraic Geometry

Day 3 - Software Demonstrations and Open Problems

Day 4 - Applied Algebraic Geometry

Day 5 - Real Algebraic Geometry

Additionally, this event coincides with a celebration of Frank Sottile's contributions to the world of computational enumerative geometry as well as his 60th birthday.