The spectrum of coupled random matrices.
Hermitian, symmetric and symplectic random ensembles: PDEs for the distribution of the spectrum.
Matrix Integrals, Toda Symmetries, Virasoro Constraints and Orthogonal Polynomials
The Spectrum of Hill's Equation.
The Algebraic Integrability of Geodesic Flow on S0(4).
The Lagrange rigid body motion
We discuss the motion of the three-dimensional rigid body about a fixed point under the influence of gravity, more specifically from the point of view of its symplectic structures and its constants of the motion. An obvious symmetry reduces the problem to a Hamiltonian flow on a four-dimensional submanifold of ; they are the customary Euler-Poisson equations. This symplectic manifold can also be regarded as a coadjoint orbit of the Lie algebra of the semi-direct product group with its natural...
Limit matrices for the Toda flow and periodic flags for loop groups.
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