We offer 3.5-year PhD positions in mathematics and theoretical computer science. Applicants should have or expect to gain at least the equivalent of a 2.1 BSc/MSc in a relevant subject area and must satisfy RCUK residency rules for the full studentship (fees + stipend). Deadline: 28 February 2015, but applications are processed as they are received. Research team: Mathematical Foundations of Computation (Proofs, Categories, Semantics, Geometry, Computer Algebra and Cryptography) http://www.bath.ac.uk/comp-sci/research/mathematical-foundations/ Institution: University of Bath Potential supervisors: Russell Bradford http://is.gd/Y5XgCG Paola Bruscoli http://cs.bath.ac.uk/pb James Davenport http://staff.bath.ac.uk/masjhd Alessio Guglielmi http://alessio.guglielmi.name Willem Heijltjes http://cs.bath.ac.uk/~wbh22 Jim Laird http://cs.bath.ac.uk/~jl317 Guy McCusker http://cs.bath.ac.uk/~gam23 John Power http://is.gd/U82foN Nicolai Vorobjov http://people.bath.ac.uk/masnnv/ To apply, including information on prerequisites: http://www.bath.ac.uk/science/graduate-school/research-programmes/phd-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 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 and utilising, among other tools, category theory and algebraic geometry. These theories are closely related, they benefit from mutual interaction and they are well represented in our team. 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 on the logic side, and regular chains, cylindrical algebraic decomposition and monotone sets on the algebra/geometry side. 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. To obtain more information and to apply, please follow the link above. Feel free to contact Alessio Guglielmi (A.Guglielmi AT Bath.Ac.UK) for any questions about a PhD in Proofs, Categories and Semantics, or contact James Davenport (J.H.Davenport AT Bath.Ac.UK) for a PhD in Geometry, Computer Algebra and Cryptography.