Triangle Seminars
Monday, 5 Nov 2007
Open/closed topological field theory and topological gravity
Ezra Getzler
Tuesday, 6 Nov 2007
Asymptotics of biorthogonal polynomials associated to the two-matrix model
Maurice Duits
(KU Leuven)
Abstract:
I will report on some joint work with Arno Kujlaars on the two-matrix model in random matrix theory. In this model one is interested in the eigenvalue statistics for two NxN hermitian Matrices, M1 and M2, taken random from exp(-NTrV(M1)-NTrW(M2)+tauTrM1M2)dM1dM2. Here V and W are two polynomials of even degree and tau is called coupling contant.
The eigenvalues statistics of M1 and M2 can be expressed in terms of certain biorthogonal polynomials. Therefore, if one can find asymptoticss for the biorthogonal polynomials then one also knowns the asymptotics for the eigenvalue statistics. Asymptotic results for the biorthogonal polynomials are known in the physics literature, however, they are without rigurous proofs. I will discuss a rigorous approach for a special case. The key element is a Deift-Zhou steepest descent analysis for a 4x4 Riemann-Hilbert problem.
I will report on some joint work with Arno Kujlaars on the two-matrix model in random matrix theory. In this model one is interested in the eigenvalue statistics for two NxN hermitian Matrices, M1 and M2, taken random from exp(-NTrV(M1)-NTrW(M2)+tauTrM1M2)dM1dM2. Here V and W are two polynomials of even degree and tau is called coupling contant.
The eigenvalues statistics of M1 and M2 can be expressed in terms of certain biorthogonal polynomials. Therefore, if one can find asymptoticss for the biorthogonal polynomials then one also knowns the asymptotics for the eigenvalue statistics. Asymptotic results for the biorthogonal polynomials are known in the physics literature, however, they are without rigurous proofs. I will discuss a rigorous approach for a special case. The key element is a Deift-Zhou steepest descent analysis for a 4x4 Riemann-Hilbert problem.
Posted by: brunel
Wednesday, 7 Nov 2007
Berry's Phase, Supersymmetry and D-Branes
📍 London
David Tong
(DAMTP)
Abstract:
Berry's phase is a beautiful and simple idea in quantum mechanics, with application to many areas of condensed matter physics. After reviewing the non-Abelian version of Berry's phase, I will explain how this concept naturally fits together with supersymmetry. I will then show how to compute Berry's phase in D-brane systems, using both traditional quantum mechanics, as well as AdS/CFT techniques.
Berry's phase is a beautiful and simple idea in quantum mechanics, with application to many areas of condensed matter physics. After reviewing the non-Abelian version of Berry's phase, I will explain how this concept naturally fits together with supersymmetry. I will then show how to compute Berry's phase in D-brane systems, using both traditional quantum mechanics, as well as AdS/CFT techniques.
Posted by: KCL
Strings on conifolds from strong coupling
David Berenstein
(University of California, Santa Barbara)
Abstract:
I will talk about a new method of performing a strong coupling expansion for many superconformal field theories in four dimensions, in particular those that are relavant for the AdS/CFT correspondence. I will first explain the methods for the case of N=4 SYM, as well as what calculations can be done (both analytically and numerically) and I will show how they compare with the dual AdS geometry. I will then explain what generalizations are required for other setups and what new field theory calculations can be done with these methods that were not available before.
I will talk about a new method of performing a strong coupling expansion for many superconformal field theories in four dimensions, in particular those that are relavant for the AdS/CFT correspondence. I will first explain the methods for the case of N=4 SYM, as well as what calculations can be done (both analytically and numerically) and I will show how they compare with the dual AdS geometry. I will then explain what generalizations are required for other setups and what new field theory calculations can be done with these methods that were not available before.
Posted by: IC