We intend to provide an introduction to various important aspects of Algebraic Geometry, including applications of current interest. The courses during the first week will focus on the following subjects:
- Intersection Theory.
- Deformation Theory.
- Introduction to Tropical Algebraic Geometry.
- Algebro-Geometric Codes.
The first two topics are basic in algebraic geometry and have applications to physics, to dynamical systems, and to effective computations. The third topic is an emerging field, with applications to mirror symmetry, to degenerations of algebraic varieties, to algebraic statistics, etc. The fourth topic is an established application of the theory of algebraic curves over finite fields. The second week will be devoted to a variety of research lectures by leading specialists.