Triangle Seminars
Tuesday, 7 Apr 2009
Cluster Mutation-Periodic Quivers and Associated Laurent Sequences
Allan Fordy
(University of Leeds)
Abstract:
We consider quivers/skew-symmetric matrices under the action of mutation (in the cluster algebra sense). We classify those which are isomorphic to their own mutation via a cycle
permuting all the vertices, and give families of quivers which have higher periodicity. The periodicity means that sequences given by recurrence relations arise in a natural way from the associated cluster algebras. We present a number of interesting, new nonlinear recurrences, necessarily with the Laurent property, of both the real line and the plane. In particular, we show that some of these recurrences can be
linearised and, with certain initial conditions, give integer sequences which contain all solutions of some particular Pell equations.
We consider quivers/skew-symmetric matrices under the action of mutation (in the cluster algebra sense). We classify those which are isomorphic to their own mutation via a cycle
permuting all the vertices, and give families of quivers which have higher periodicity. The periodicity means that sequences given by recurrence relations arise in a natural way from the associated cluster algebras. We present a number of interesting, new nonlinear recurrences, necessarily with the Laurent property, of both the real line and the plane. In particular, we show that some of these recurrences can be
linearised and, with certain initial conditions, give integer sequences which contain all solutions of some particular Pell equations.
Posted by: KCL
Spectral statistics of a pseudo-integrable map: the general case
Remy Dubertrand
(Bristol)
Abstract:
It is well established numerically that the spectral statistics of
pseudo-integrable models differ considerably from the reference statistics of
integrable and chaotic systems.
In a previous paper by Bogomolny and Schmit the statistical properties of a
certain quantized pseudo-integrable map had been calculated analytically but
only for a special sequence of matrix dimensions. This talk aims at describing
the method in order to obtain the spectral
statistics of the same quantum map for all matrix dimensions.
It is well established numerically that the spectral statistics of
pseudo-integrable models differ considerably from the reference statistics of
integrable and chaotic systems.
In a previous paper by Bogomolny and Schmit the statistical properties of a
certain quantized pseudo-integrable map had been calculated analytically but
only for a special sequence of matrix dimensions. This talk aims at describing
the method in order to obtain the spectral
statistics of the same quantum map for all matrix dimensions.
Posted by: brunel