Hendrik Lenstra: Lattices with symmetry

It is a notoriouly difficult algorithmic problem to decide 
whether a given lattice admits an orthonormal basis. However, 
this problem becomes doable if the lattice is given along with
a suitably large abelian group of symmetries. The lecture, which
does not presuppose any specialized knowledge, is devoted to a
precise formulation of this result and to an outline of the
algorithm that underlies its proof. One of the main ingredients
is an elegant algorithmic technique that C. Gentry and M. Szydlo
introduced several years ago in the context of cryptography, but
that can be recast in algebraic language. (Joint work with Alice
Silverberg and Ren\'e Schoof.)