Triangulated Categories in Algebra, Combinatorics, Geometry, and Topology

Categories are high level mathematical structures which consist of objects and morphisms.  For example, there is a category consisting of topological spaces and continuous maps, which provides a framework for all questions on topological spaces.  Passing to stable homotopy and inverting the suspension turns this into a triangulated category, which is equipped with additional structure in the form of so-called triangles.  These are diagrams mimicking the long exact sequences known from algebraic topology.

Triangulated categories are found in algebra, combinatorics, geometry, and topology, and each of these areas has developed its own tools for their study.  Several breakthroughs have been accomplished by importing tools for the study of triangulated categories from one area to another.

The proposed programme will catalyze further breakthroughs by bringing together a critical mass of senior mathematicians, as well as promising junior researchers, who use triangulated categories in diverse branches of mathematics.  This will allow new bridges to be built between researchers using triangulated categories, providing new venues for methods to be imported.