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About Enrage 
 
   

  

  

Progress in the sciences is driven by the urge to push the limits of our understanding of the physical
world. The unprecedented advances of the last century are now culminating in a collective search
by theoretical physicists for the most fundamental building blocks of space, time and matter, and a
unified description of their interactions. In trying to formulate a quantum theory of physics at the
most extreme scales, there is mounting evidence that special, socalled nonperturbative methods
are being called for. These take into account that spacetime at the Planck scale is not well
approximated by the fixed, flat Minkowski space which provides the setting for standard quantum
field theory at much lower energies. Although numerous nonperturbative aspects of superstring
theories have been uncovered in recent years, and backgroundindependent formulations of quantum
gravity are being explored, a complete and fully nonperturbative construction of these theories is
still lacking. The situation is not unfamiliar from quantum chromodynamics, where powerful lattice
methods have been developed over time, but where we still lack a deeper theoretical understanding
of nonperturbative properties such as confinement.
A primary focus of the network ENRAGE is the further systematic development of an
already existing set of nonperturbative analytic and numerical tools from the theory of discrete
random geometries, and their application to some of these fundamental problems. There is a
coherent body of knowledge, especially on the dynamics of lowerdimensional geometries (graphs
and surfaces) and the closely related theory of random matrices, to which many of our network
members have made seminal contributions. These methods are rooted in quantum field theory and
the theory of critical phenomena. They are ideally suited for a nonperturbative description of
quantumgravitational and string theories, because they do not require any a priori distinguished
background geometry. Pioneering advances have already been made by network members in the
study of the critical behaviour of higherdimensional random geometries.
It turns out that the very same methods are suited for the description of a much wider range
of phenomena, from condensed matter physics, through the dynamics of networks, to biological
systems, as well as areas of pure mathematics, and the study of such topics provides a second major
focus for the network's research. The training of young researchers in the use of these highly versatile
tools  for which there is already a proven track record  will prepare them for careers not just in
physics, but in biology, information technology, computer science, finance and economics. Previous
EC networks involving some of the teams in the current network have witnessed a substantive
amount of crossfertilization and fruitful collaborations
between experts on various methodological and applied aspects of random geometry, going far
beyond the scope of any single subdiscipline of theoretical physics, and not easily accommodated
within current institutional structures. The joint network activities provide our young researchers
with a unique perspective stretching beyond the boundaries of their specific discipline.
ENRAGE draws in expertise on random geometry and random matrices from all over
Europe and beyond, while keeping a strong scientific focus on formulating a nonperturbative description of
quantum gravity and string theory using discretized random geometries and applying these methods
in the study of other statistical mechanical systems and networks. The previous networks have led
to the formulation of such new concepts as the Gonihedric string model, Lorentzian dynamical
triangulations, new numerical algorithms for the study of random geometries and the application
of quantum field theory methods to the study of networks. Building on these successes,
there is every reason to expect similar
advances with the current collaboration.


