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This volume contains the proceedings of two AMS Special Sessions `Geometric and Algebraic Aspects of Representation Theory' and `Quantum Groups and Noncommutative Algebraic Geometry' held October 13-14, 2012, at Tulane University, New Orleans, Louisiana, USA. Included in this volume are original research and some survey articles on various aspects of representations of algebras including Kac-Moody algebras, Lie superalgebras, quantum groups, toroidal algebras, Leibniz algebras and their connections with other areas of mathematics and mathematical physics.