Date: Tuesday, April 17, 2012
Title: Small generators for Sarithmetic groups
Abstract: Pell's equation for a squarefree integer d > 0 is x^2  d y^2 = 1. One expects (though it has not been proved) that there is no polynomial in d which bounds the sizes of the minimal positive solutions x and y to this equation. This illustrates the fact that in general, one expects any generating set for the unit group of a number field to include a unit of large height relative to the discriminant of the field. A surprising discovery of H. W. Lenstra, Jr., was that one can find generators of small height for groups of Sunits. These groups lie between the units and the full multiplicative group of the field. I will discuss joint work with Matt Stover on generalizing Lenstra's results from Sunits to the Sintegral points of linear algebraic groups. This has applications to finding presentations for such groups and to the congruence subgroup problem.
Speaker: Ted Chinburg
Institution: Univ of Penn
