The main scientific topics for the fourth conference in this series of Canada-Mexico-USA conferences will be geometric, algebraic and homological methods in representation theory, representation theoretic and homological properties of noncommutative algebras, and the investigation of those problems using categorical methods. The talks will cover some of the most recent trends including: cluster algebras, monoidal and additive categorifications, quantum symmetries, finite tensor categories, representations of quantized affine Kac-Moody algebras, Calabi-Yau algebras and triangulated categories, Hopfological algebra, web approaches to modular representation theory, and representation theoretic aspects of Heegaard-Floer homology.