Toric methods in geometry, arithmetics and dynamics

In recent years, toric geometry has experienced a rapid growth with a wealth of new results and connections with other areas of mathematics like arithmetic geometry and number theory, dynamical systems, non­ Archimedean and tropical geometry, mirror symmetry and birational geometry, This adds to the more classical connections to combinatorics, computer algebra and singularity theory among others, and applications to areas of science like mathematical biology and chemistry. At the same time, the concrete and explicit nature of toric varieties makes them a perfect entrance door to higher dimensional algebraic geometry.

The main purpose of this research school is to motivate and train Latin American students and young researchers in these subjects. It will consist of 6 courses of 6h each, all of them delivered by well­ recognized specialists from Argentina, USA, France and Spain. These courses will cover a basic introduction to toric varieties, followed by more advanced courses on the topological aspects, singularities, dynamical systems, non­-Archimidean and tropical geometry, and arithmetic geometry of toric varieties. In addition, we plan a series of 10 survey talks delivered by members of our scientific committee and other invited researchers from Latin America, USA and Spain.