Lattices, Perfects lattices, Voronoi reduction theory, modular forms, computations of isometries and automorphisms 2

Appears in collection : Summer School 2022 - Cohomology, Geometry and Explicit number theory (COGENT)

The talks of Coulangeon will introduce the notion of perfect, eutactic and extreme lattices and the Voronoi's algorithm to enumerate perfect lattices (both Eulcidean and Hermitian). The talk of Nebe will build upon these notions, introduce Boris Venkov's notion of strongly perfect lattices and show that these are perfect and eutactic and hence extreme. We will show how to construct such lattices using representation theory of finite groups and modular forms.