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, ...

This is a preview. Log in through your library . Journal Information The Journal of Symbolic Logic (JSL) was founded in 1936 and it has become the leading research journal in the field. It is issued ...

The original version of this story appeared in Quanta Magazine. The French scholar Pierre-Simon Laplace crisply articulated his expectation that the universe was fully knowable in 1814, asserting that ...

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 ...

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 ...

We study the first order theory of function fields in the language of fields by using fundamental results on curves in algebraic geometry. We give some applications; for example, using a theorem of G.