Efficient and Natural Proof Systems
Proofs and algorithms are everyday objects in our discipline, but they are still very mysterious. Suffice to say that we are currently unable to decide whether two given proofs or two given algorithms are the same; this is an old problem that dates back to Hilbert. Also, proofs and algorithms are intimately connected in the most famous open problem in mathematics: P vs NP.
We make progress by trying to unveil the fundamental structure behind proofs and algorithms, what we call their semantics. In other words, we are interested in the following questions:
What is a proof?
What is an algorithm?
How can we define them so that they have efficient and natural semantics?
The questions above are interesting in their own right, but we note that answering them will enable technological advances of great impact on the society and the economy. For example, it will be possible to build a worldwide, universal tool for developing, validating, communicating and teaching mathematics. Also, quickly producing provably bug-free and secure software will become possible, so solving one of the most complex and important open engineering problems.
In order to understand proofs and algorithms we create new mathematics starting from proof theory and semantics. The methods we use are mostly discrete, algebraic and combinatorial, but there is a growing geometrical component. The recent advances which our methods are mostly based on are linear logic, game semantics and deep inference.
You can find more information at
Our group is very well financed via several grants. Thanks to our international relations, working with us means having a truly multicultural experience together with all the researchers at the forefront of this worldwide research effort. As a result, all our graduates work and publish at the highest level. The facilities at the University of Bath are outstanding and the city is so beautiful that UNESCO recognises it as a World Heritage Site.
Feel free to contact Alessio Guglielmi (A.Guglielmi AT Bath.Ac.UK).
We welcome all year round applications from self-funded candidates and candidates who can source their own funding.
To apply, including information on prerequisites:
Please note: the application deadline is 30th April 2015 but studentships might be allocated before the deadline if suitable candidates have been found.