Triangle Seminars
Tuesday, 8 May 2007
Critical edge behavior in unitary random matrix ensembles and the thirty fourth Painleve transcendent
Jorgen Ostensson
(Leuven)
Abstract:
I will discuss a recent work which concerns the critical behavior of eigenvalues in ensembles
1/Z(n,N) det M(2 alpha) exp(-N Tr V(M)) dM with
alpha greater than -1/2, where the factor det M(2alpha) induces critical eigenvalue behavior near the origin. Supposing that the limiting mean eigenvalue density associated with V is
regular, and that the origin is a right endpoint of its support, one can compute (using the Deift-Zhou steepest-descent method) the limiting eigenvalue correlation kernel in the double scaling limit as n, N to infinity such that n(2/3) (n/N-1) = O(1). It turns out that the limiting kernel can be described through a distinguished solution of the thirty fourth Painleve equation. This solution is related to a particular solution of the Painleve II equation,
which however is different from the usual Hastings-McLeod solution.
The talk is based on joint work with Alexander Its and Arno Kuijlaars.
I will discuss a recent work which concerns the critical behavior of eigenvalues in ensembles
1/Z(n,N) det M(2 alpha) exp(-N Tr V(M)) dM with
alpha greater than -1/2, where the factor det M(2alpha) induces critical eigenvalue behavior near the origin. Supposing that the limiting mean eigenvalue density associated with V is
regular, and that the origin is a right endpoint of its support, one can compute (using the Deift-Zhou steepest-descent method) the limiting eigenvalue correlation kernel in the double scaling limit as n, N to infinity such that n(2/3) (n/N-1) = O(1). It turns out that the limiting kernel can be described through a distinguished solution of the thirty fourth Painleve equation. This solution is related to a particular solution of the Painleve II equation,
which however is different from the usual Hastings-McLeod solution.
The talk is based on joint work with Alexander Its and Arno Kuijlaars.
Posted by: brunel
Thursday, 10 May 2007
The twistor programme and twistor strings (From twistor-strings to quantum gravity)
Lionel Mason
(Oxford University)
Abstract:
The twistor programme was introduced by Roger Penrose as an approach to quantum gravity in which twistor space should provide the primary geometric background for physics from which space-time should emerge. This talk will review the programme, i.e., the early successes in formulating the self-dual parts of Yang-Mills and gravity on twistor space. It will go on to review the impact of twistor-string theory, in giving at least a perturbative approach to full Yang Mills and conformal gravity, and outline arguments that prove the equivalence between the twistor-string models and the space-time theories. Finally, twistor-string models for Einstein gravity will be reviewed.
The twistor programme was introduced by Roger Penrose as an approach to quantum gravity in which twistor space should provide the primary geometric background for physics from which space-time should emerge. This talk will review the programme, i.e., the early successes in formulating the self-dual parts of Yang-Mills and gravity on twistor space. It will go on to review the impact of twistor-string theory, in giving at least a perturbative approach to full Yang Mills and conformal gravity, and outline arguments that prove the equivalence between the twistor-string models and the space-time theories. Finally, twistor-string models for Einstein gravity will be reviewed.
Posted by: IC
Completing MHV Rules via Equivalence Theorem Evasion
Tim Morris
(Southampton)