My main interests are on the (GIT) moduli spaces of representations of quivers with relations, including 1. Classification of moduli of quiver representations 2. Wall crossing formulas for spaces and their coherent sheaves 3. Counting formulas including non-commutative DT-invariants. I would like to understand their geometry from a categorical point of view. The theory has applications in representation theory, cluster algebra, Schubert calculus, algebraic geometry, and number theory. In series of paper “Moduli and tilting”, I use birational geometry and tilting theory to study 1 and 2. In another series “Counting using Hall algebras”, I focus on 3 with many applications.