Topology & Geometric Group Theory Seminar

Spring 2010

1:30 – 2:30, Malott 203

Tuesday, February 16

This talk is intended as an overview of my joint work with R. Kravchenko and M. Mazur (arXiv:1001.2873). That preprint addresses the following 2 related topics.

1. Let R be an order in a number field. Let A be an R-algebra whose additive R-module is free of finite rank. What is the probability that k random elements of A generate it as an R-algebra? After making this question precise I will show that it has an interesting answer which can be interpreted as a local-global principle.
2. We would like to calculate the smallest number of generators of such an algebra. We have complete answers for the R-algebras M₂(R)^k and M₃(R)^k, where R is the ring of integers in a number field and k is a positive integer.