[TYPES/announce] PhD Research Project: Efficient and Natural Proof Systems
Alessio Guglielmi
web.alessio.guglielmi at gmail.com
Mon Mar 18 13:40:20 EDT 2013
Hello, could you please help us advertise the
following position? Ciao, -Alessio
*** PhD Studentship ***
Research Project: Efficient and Natural Proof Systems
<http://www.cs.bath.ac.uk/ag/ENPS/>
Institution: University of Bath - Department of Computer Science
PhD Supervisors: Alessio Guglielmi and/or Guy McCusker
<http://alessio.guglielmi.name>
<http://www.cs.bath.ac.uk/~gam23/>
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: <http://is.gd/Qf2qpd>). 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 <http://is.gd/7XYPbt>). 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 <http://is.gd/leM81c> [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 <http://is.gd/ZUlZ5n>).
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: <http://is.gd/RCaAvA/>.
Feel free to contact Alessio Guglielmi for any
question you might have about this position.
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