COSIC seminar 'Algorithmic aspects of algebraic lattices' (Thomas Espitau)

COSIC seminar – Algorithmic aspects of algebraic lattices – Thomas Espitau (Paris 6 Sorbonne university)

Lattices are mathematical objects generalizing the concrete idea of grid embedded in the plane. They play a fundamental role in the study of various subfields of mathematics and computer science, in particular, algebraic number theory and cryptography. This talk deals with so-called “algebraic” lattices, that is, constructed above a maximal order of a number field, with a particular emphasis on computational methods. After seeing lattice reduction in an uniform framework based on filtrations, we will aim at developing effective algorithms for the reduction of lattices over cyclotomic fields, in particular by exploiting their natural recursive and symplectic structure.