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, ...

Many classes of structures have natural functions and relations on them: concatenation of linear orders, direct product of groups, disjoint union of equivalence structures, and so on. Here, we study ...

In mathematics, there are easily described problems that are very challenging to solve. A great example of this was made famous by Christian Goldbach in 1742. He discovered that no matter what even ...

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 ...

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 ...