Fyrirlesari: Willem Westra, research scientist University of Iceland.
Titill: Enumerating planar maps by ordinary integrals.
Ágrip: The enumeration of planar maps is a classical problem in the field of combinatorics. In the sixties Tutte became famous by giving a solution in terms of generating functions. Later-on physicists discovered that the planar maps are naturally counted by the large N asymptotic expansion of integrals over N x N Hermitian matrices.
In this talk I show that one can count planar maps even with ordinary integrals. Moreover, we present a new scaling limit where the random planar maps describe continuum random surfaces. In this new limit the continuum surfaces are much better behaved in comparison to the continuum surfaces that one obtains from the well known large N double scaling limit.
Titill: Enumerating planar maps by ordinary integrals.
Ágrip: The enumeration of planar maps is a classical problem in the field of combinatorics. In the sixties Tutte became famous by giving a solution in terms of generating functions. Later-on physicists discovered that the planar maps are naturally counted by the large N asymptotic expansion of integrals over N x N Hermitian matrices.
In this talk I show that one can count planar maps even with ordinary integrals. Moreover, we present a new scaling limit where the random planar maps describe continuum random surfaces. In this new limit the continuum surfaces are much better behaved in comparison to the continuum surfaces that one obtains from the well known large N double scaling limit.
