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Let $\Lambda$ be a finite-dimensional algebra over a fixed algebraically closed field $\mathbf{k}$ of arbitrary characteristic, and let $V$ be a finitely generated $\Lambda$-module. It follows from results previously obtained by F.M. Bleher and the third author that $V$ has a well-defined versal deformation ring $R(\Lambda, V)$, which is a complete local commutative Noetherian $\mathbf{k}$-algebra with residue field $\mathbf{k}$. The third author also proved that if $\Lambda$ is a Gorenstein $\mathbf{k}$-algebra and $V$ is a Cohen-Macaulay $\Lambda$-module whose stable endomorphism ring is isomorphic to $\mathbf{k}$, then $R(\Lambda, V)$ is universal. In this article we prove that the isomorphism class of a versal deformation ring is preserved under singular equivalence of Morita type between Gorenstein $\mathbf{k}$-algebras., Comment: Sensitive error found in one of the proofs

We determine the derived representation types of algebras with radical square zero and give a description of the indecomposable objects in their bounded derived categories., 8 pages

We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. The proof is based on the technique of matrix problems (boxes and reduction algorithm). It implies, in particular, that any degeneration of a derived wild algebra is derived wild; respectively, any deformation of a derived tame algebra is derived tame., 10 pages

We investigate weight modules for finite and infinite Weyl algebras, classifying all such simple modules. We also study the representation type of the blocks of locally-finite weight module categories and describe indecomposable modules in tame blocks.