3.5-year PhD positions from October 2015 at the University of Bath

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-comp=
uter-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.