Recent Developments in Representation Theory

Contains selected expository lectures delivered at the Maurice Auslander Distinguished Lectures and International Conference, held in May 2014. Three of the five lectures in this volume deal with the Catalan combinatorics, the combinatorics of Gelfand-Zetlin polytopes, and the combinatorics of tilting modules.

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This volume contains selected expository lectures delivered at the Maurice Auslander Distinguished Lectures and International Conference, held May 1-6, 2014, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Several significant developments of the last decade in representation theory of finite-dimensional algebras are related to combinatorics. Three of the five lectures in this volume deal, respectively, with the Catalan combinatorics, the combinatorics of Gelfand-Zetlin polytopes, and the combinatorics of tilting modules. The remaining papers present history and recent advances in the study of left orders in left Artinian rings and a survey on invariant theory of Artin-Schelter regular algebras.