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Efficient and Natural Proofs and Algorithms

Project Description

The University of Bath is inviting applications for the following PhD project under the supervision of Dr Alessio Guglielmi and Dr Willem Heijltjes in the Department of Computer Science.

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 answering them will enable technological advances of great impact on 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.

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 multicultural experience 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. For example, one of our recent PhDs, Anupam Das, has won a prestigious UKRI Future Leaders Fellowship in 2019, worth £1.5M. The facilities at the University of Bath are outstanding and the city is so beautiful that UNESCO recognises it as a World Heritage Site.

Informal enquiries are welcomed and should be addressed to:
Alessio Guglielmi
Willem Heijltjes

Candidate requirements:

Applicants should hold, or expect to gain, a First Class or Upper Second Class Honours degree in Mathematics or Computer Science, or the equivalent from an overseas university. A master’s level qualification would also be advantageous.

How to apply:

Formal applications should be made via the University of Bath’s online application form for a PhD in Computer Science:

More information about applying for a PhD at Bath may be found here:

Anticipated start date: 28 September 2020.

Funding Notes

UK and EU students who have been ordinarily resident in the UK since September 2017 will be considered for an EPSRC DTP studentship. Funding will cover UK/EU tuition fees, maintenance at the UKRI Doctoral Stipend rate (£15,009 per annum, 2019/20 rate) and a training support grant of £1,000 per annum for 3.5 years.

For more information on eligibility: View Website.

We welcome all-year-round applications from self-funding candidates and candidates who can source their own external sponsorship.

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