The Symplectic Penrose Kite

The purpose of this article is to view the Penrose kite from the perspective of symplectic geometry.Comment: 24 pages, 7 figures, minor changes in last version, to appear in Comm. Math. Phys

Probabilistic methods for discrete nonlinear Schr\"odinger equations

We show that the thermodynamics of the focusing cubic discrete nonlinear Schrodinger equation are exactly solvable in dimensions three and higher. A number of explicit formulas are derived.Comment: 30 pages, 2 figures. To appear in Comm. Pure Appl. Mat