From my work on the number-theoretic features of string theory connected with the algebraic geometry of the strings' world-sheets, I have been led to the study of certain two-dimensional integrable models which exhibit similar number-theoretic features. This has yielded new results on scattering processes in two-dimensional integrable quantum field theories. It has long been known that in such theories there is no particle production and the scattering of two particles determines the scattering of three or more particles. In a very large class of such theories, it turns out that even the input two-particle scattering is determined by simple considerations of quantum-geometry.

Geometries involving direct products of 4-dimensional anti-de Sitter (AdS) space with a 7-dimensional compact Einstein manifold, and of 7-dimensional AdS space with a 4-dimensional compact Einstein manifold which have appeared in the context of solutions of 11-dimensional supergravity found with M. Rubin, have recently been connected by Maldacena with conformal field theory in 3 and 6 dimensions. For certain cases this connection (and similar connections in other dimensions) have been studied in quite some detail by many authors. I am considering certain solutions of this type involving minimal supersymmetry or no supersymmetry at all.

We have constructed gravitational analogs of Born's nonlinear electrodynamics. In a very different vein we studied the implications of discrete scale invariance in certain rupture phenomena such as stock market crashes.