Quantum Mathematics

One hundred years of quantum theory have uncovered a vast wealth of mathematical ideas and applications, often in seemly disconnected subjects. These range from the subtle and intricate relations between quantum theory and classical mechanics, deformations of classical geometry, new tools in topology and arithmetic geometry, a myriad of exciting algebraic structures and the deep mysteries of quantum field theory itself. 

The idea of the theme is, to paraphrase Freeman Dyson, to make the most of the wonderful mathematical opportunities of quantum theory.