The spectral gap is one of the most important physical properties of a quantum many-body system, determining much of its low-energy physics. Gapped systems exhibit non-critical behaviour (for example, ...

We give a new proof of the following result (originally due to Linial and Post): it is undecidable whether a given calculus, that is a finite set of propositional formulas together with the rules of ...

This course gives an introduction to the mathematical foundations of computation. The course will look at Turing machines, universal computation, the Church-Turing thesis, the halting problem and ...