Homological and geometric methods in algebra

This is a project dealing with basic research in algebra/algebraic geometry, in particular connections and interplay with very different topics. The focus is on homological, geometrical and combinatorial aspects, and some of the topics also have connectio ns with topology and combinatorics. The central topics in the project are Hochschild cohomology and support varieties, geometry of quiver representations, tilting theory, cluster categories and cluster algebras, stability in triangulated categories, categ ories of sheaves on the varieties of pure spinors and hereditary categories. Hochschild cohomology and triangulated categories are important in many different parts of algebra/algebraic geometry and in topology, and hence an investigation of these topics leads to interaction between researchers with different background, and hence new connections between different areas. Hereditary categories are of interest both for finite dimensional algebras and noncommutative algebraic geometry. The study of cluster c ombinatorics has proved to be important in various areas of mathematics and physics. The study of geometry of quiver representations gives a link between the theory of finite dimensional algebras and algebraic geometry. The theory of pure spinors may give new links between algebraic geometry and Lie superalgebras.