Derived-tame algebras

I shall first give a survey of known classes of derived-tame finite dimensional algebras (gentle, skew-gentle) explaing the origin of the corresponding combinatorics of indecomposable objects from the point of view of matrix problems (representations of bunches of (semi-)chains). Then I discuss another class of derived-tame algebras which can be approached by a similar method. This is a joint work in progress with Yuriy Drozd.