Modular Index Theory

This project will apply and extend recent advances in index theory to KMS states. Index theory is concerned with the existence and number of solutions to differential equations. KMS states generalise the notion of trace in mathematics, and the role of traces in index theory is to measure the dimension of the space of solutions of an equation. The index theory we will develop for KMS states is called modular index theory. Novel invariants of operator algebras can thus be obtained, with applications to both mathematics and many particle physics.