Claus Michael Ringel(林格尔)

My research is devoted to representations of finite-dimensional associative algebras as they arise in many parts of mathematics and mathematical physics. The target is to describe the general structure of these module categories, their derived categories as well as related categories such as the homotopy category of perfect complexes or the category of Gorenstein-projective modules. In this way, one tries to obtain a conceptual framework for dealing with matrix problems. The invariants which have to be studied concern combinatorial, homological or geometrical properties and provide relations to Lie theory, combinatorial algebra, commutative ring theory and algebraic geometry. The representation theory of quivers may be used in order to construct quantum groups and cluster algebras.