Hochschild cohomology and deformation theory of triangulated categories (R-6675)

Non-commutative algebraic geometry is a rapidly growing subject with new striking applications continuously appearing. For example in string theory mirror partners are often non-commutative. As another example it is now known that many features of the minimal model program in algebraic geometry can be explained through non-commutative phenomena acting behind the scenes. Unfortunately it is in general difficult to transplant geometric intuition to the non-commutative context. Indeed the very definition of a non-commutative space is very abstract and quite remote from the idea of a topological space with functions on them. Nonetheless some types of noncommutative spaces are amenable to geometric reasoning and these can serve as a model to develop more general 'non-commutative intuition'. Non-commutative spaces that are 'close' to commutative spaces may be highly non-trivial by themselves, as the now classical example of non-commutative projective planes shows. Yet such 'deformed' spaces can be particularly easy to understand from a geometric point of view. Therefore in this project we aim to develop techniques to classify and study deformed spaces.

Keywords:NON-COMMUTATIVE ALGEBRAIC GEOMETRY, NON-COMMUTATIVE RINGS

Disciplines:Algebra