We propose a research in representation theory of associative algebras which aims at establishing new connections between different theoretical aspects. We will mainly deal with a k-algebra A which will often be assumed to be finite dimensional over an algebraically closed field k and will thus be determined by a quiver with possible relations.
Our goal is to understand the interplay between several combinatorial or topological structures associated with A, such as the lattice of torsion pairs in the
category of A-modules, the lattice of ring epimorphisms with domain A, the Ziegler spectrum of A, and the wall and chamber structure induced by stability conditions over A.
Fundamental tools for our investigations include silting theory, and in particular a new approach to mutation in triangulated categories via the concept of a large (i.e. not necessarily compact) cosilting object, and methods from geometric representation theory.
The project is in collaboration with Research Units at the Universites of Padova, Roma-Sapienza and Torino.
