Understanding the highly entangled states and complex dynamics of quantum many-body systems is a core problem of modern condensed matter physics that will require the development of new mathematics.

Recent years have revealed deep connections with concepts in mathematics ranging from topological field theory, homotopy theory, category theory, operator algebras, tensor networks, to complexity theory, each of which is a rich and evolving subject in its own right. This school brings students together with experts in these fields with the aim of laying a broad yet solid foundation for approaching quantum matter physics and its cross-pollination with modern mathematics. The mutually beneficial exchange of ideas between mathematics and physics has a long and successful history. Many breakthroughs in mathematics since 1950 have been inspired by quantum field theory and string theory. Quantum matter has the potential to play a similarly prominent role in 21st-century mathematics.

The school is aimed at advanced undergraduate or graduate students, who have taken some basic courses in algebra and topology. We also encourage to apply physics students with strong mathematical background.