The past decade have seen important progress by mathematicians and physicists alike on a class of geometric objects called symplectic singularities. On the math side, they lie at the crossroad between algebraic geometry and representation theory, while from the physical perspective they arise as moduli space for supersymmetric quantum field theories. As such, they can be studied using tools from string theories and branes. The first week will be a summer school, the second week will be a workshop. Participants can attend the first week, the second week, or both.