The goal of this mini-conference is to explore the newly found connections between various dualities in physics (such as the S-duality in 4D supersymmetric gauge theory and Mirror Symmetry of 2D sigma models) and in mathematics (geometric Langlands Program). Among the topics considered will be the work of Gaiotto and Witten on duality of boundary conditions in 4D super-Yang-Mills theory, as well as the wall-crossing formulas studied in mathematics by Joyce, Bridgeland, Toledano Laredo, Kontsevich, and Soibelman and in physics by Gaiotto, Neitzke, Moore, and others.