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AISB opportunities Bulletin Item

PhD student position in efficient and natural proof systems, Bath (U.K.)

*** PhD Studentship ***

Research Project: Efficient and Natural Proof Systems

Institution: University of Bath - Department of Computer Science

PhD Supervisors: Alessio Guglielmi and/or Guy McCusker

Application Deadline: 17 April 2013

Math is growing more complex each day, to the point that the assistance of 
computers is becoming necessary even for the most theoretically inclined among 
the mathematicians (see this recent article by Natalie Wolchover on Wired: 
). After centuries of producing proofs in our heads and 
then describing them in papers, we are moving fast towards a future of proofs 
conceived by humans together with computers, which in turn will guarantee their 
correctness and availability.

But what is a proof? What could a common language between humans and computers 
be? A satisfying definition of mathematical proof has proved to be a very 
elusive concept. Suffice to say that the problem of deciding whether two formal 
proofs are the same has remained open since Hilbert formulated it more than one 
hundred years ago.

Finding efficient and natural proof systems is a fascinating problem that spans 
from philosophy, through math, to computer science. There is growing evidence 
that, at its core, good solutions can be provided by geometrical ideas. Indeed, 
many mathematicians interested in the foundations of mathematics have recently 
turned to geometry.

We propose a PhD in the context of the EPSRC project `Efficient and Natural 
Proof Systems? (see at ). In this project, we will define 
a new proof system which, essentially, will represent proofs as geometric 
shapes equivalent under continuous deformation. Three areas of mathematics and 
theoretical computer science concur in the definition of these proof systems: 
categorical semantics, proof theory and proof complexity. The result of this 
project will be the completion of three decades of efforts in proof theory that 
started with linear logic and continued with deep inference (see 
 [beware, there are jokes in that page]).

We are looking for a brilliant mathematician or theoretical computer scientist 
who is not afraid of working with category theory and who has a good geometric 
intuition. We provide a fully funded three-year PhD position in the exceptional 
research environment of one of the best worldwide research groups in semantics 
and proof theory (see at ).

Your full tuition fees will be covered and you will receive a standard EPSRC 
maintenance payment of 13,726/annum (13/14 rate) for three years. Funding for 
this project is available to citizens of a number of European countries 
(including the UK). In most cases this will include all EU nationals. However 
full funding may not be available to all applicants and you should read the 
full department and project details for further information.

To apply, start here: . Feel free to contact Alessio 
Guglielmi for any question you might have about this position.