DEPARTMENT COLLOQUIUM

4/5/2006

Akshay Venkatesh
Institute for Advanced Study and New York University

Cubic fields, and dynamics on the space of rank 3 lattices

Quadratic irrationals (e.g. sqrt{13}) have periodic continued fractions, which are closely related to the arithmetic of the quadratic field Q(sqrt{13}). For cubic irrationals and cubic fields,  what is an analogue of "periodic continued fraction"? This naturally leads to the study of the dynamics mentioned in the title. In this context, I'll explain Duke's "equidistribution theorem" for quadratic fields, and the recent analogue of this theorem for cubic fields, established in joint work with M. Einsiedler,  E. Lindenstrauss and P. Michel.