Symmetric superspaces: slices, radial parts, and invariant functions / Alexander Alldridge -- Geometry of quiver Grassmannians of Dynkin type with applications to cluster algebras / Giovanni Cerulli Irelli -- Spherical varieties and perspectives in representation theory / Stéphanie Cupit-Foutou -- Categorical actions from Lusztig induction and restriction on finite general linear groups / Olivier Dudas, Michela Varagnolo, Éric Vasserot -- Homological mirror symmetry for singularities / Wolfgang Ebeling -- On the category of finite-dimensional representations of OSp$(r|2n)$: Part I / Michael Ehrig, Catharina Stroppel -- On cubes of Frobenius extensions / Ben Elias, Noah Snyder, Geordie Williamson -- On toric degenerations of flag varieties / Xin Fang, Ghislain Fourier, Peter Littelmann -- Subquotient categories of the affine category $\mathcal O$ at the critical level / Peter Fiebig -- Low-dimensional topology, low-dimensional field theory and representation theory / Jürgen Fuchs, Christoph Schweigert -- Derived categories of quasi-hereditary algebras and their derived composition series / Martin Kalck -- Dominant dimension and applications / Steffen Koenig -- Highest weight categories and strict polynomial functors. With an appendix by Cosima Aquilino / Henning Krause -- In the bocs seat: Quasi-hereditary algebras and representation type / Julian Külshammer -- From groups to clusters / Sefi Ladkani -- Semi-infinite combinatorics in representation theory / Martina Lanini -- Local-global conjectures in the representation theory of finite groups / Gunter Malle -- Bounded and semibounded representations of infinite dimensional Lie groups / Karl-Hermann Neeb -- On ideals in $\operatorname{U}(\mathfrak {sl} (\infty)), \operatorname{U}(\mathfrak {o} (\infty)), \operatorname{U}(\mathfrak {sp} (\infty))$ / Ivan Penkov, Alexey Petukhov -- Spherical varieties: applications and generalizations / Guido Pezzini -- Quiver moduli and small desingularizations of some GIT quotients / Markus Reineke -- Geometric invariant theory for principal three-dimensional subgroups acting on flag varieties / Henrik Seppänen, Valdemar V. Tsanov -- Inductive conditions for counting conjectures via character triples / Britta Späth -- Restricted rational Cherednik algebras / Ulrich Thiel -- On the existence of regular vectors / Christoph Zellner.

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From April 2009 until March 2016, the German Science Foundation supported generously the Priority Program SPP 1388 in Representation Theory. The core principles of the projects realized in the framework of the priority program have been categorification and geometrization, this is also reflected by the contributions to this volume. Apart from the articles by former postdocs supported by the priority program, the volume contains a number of invited research and survey articles, many of them are extended versions of talks given at the last joint meeting of the priority program in Bad Honnef in March 2015. This volume is covering current research topics from the representation theory of finite groups, of algebraic groups, of Lie superalgebras, of finite dimensional algebras and of infinite dimensional Lie groups. Graduate students and researchers in mathematics interested in representation theory will find this volume inspiring. It contains many stimulating contributions to the development of this broad and extremely diverse subject.