Techniques and algorithmic methods from algebraic geometry are making an impact on applied mathematics and engineering. Algebraic techniques provide new approaches to hard computational problems. They deliver exact answers desired in many applications through symbolic computation, and enhance approximate numerical solving.
The program will be structured around a course in computational algebraic geometry, treating foundational material as well as current applications. The foundations will include introductions to Gröbner bases, numerical algebraic geometry, semidefinite programming and real algebraic geometry, and tropical geometry. We will include tutorials and lab sessions on computer algebra systems. There will be several guest lectures by the leading researchers in the field.