Beth Romano

Generalizing the LLL algorithm

Given a lattice L in n-dimensional space, the Lenstra-Lenstra-Lovasz (LLL) algorithm gives a basis for L that is reduced, in a certain sense. I will talk about work in progress with Jack Thorne in which we generalize this algorithm. More specifically, we can think about the problem of lattice reduction in terms of a symmetric space for the group SL_n. In our generalization we replace SL_n with an arbitrary split reductive group. In the talk, I will give some background about the classical LLL algorithm, and I will mention how the general setting appears in number-theoretic applications.