Talk page
Title:
Approximate Lattices in Algebraic Groups
Speaker:
Abstract:
Approximate lattices in locally compact groups are approximate subgroups that are discrete and have finite co-volume. They provide natural examples of objects at the intersection of algebraic groups, ergodic theory and additive combinatorics... with a twist. Indeed, approximate lattices are note finite - rendering most of the known theory of approximate subgroups unavailable to us.
A central question arising from seminal work of Yves Meyer asks whether all approximate lattices have an arithmetic origin. After presenting a complete structure theorem for approximate lattices in algebraic groups generalising arithmeticity theorems of Margulis and Mostow, I will pinpoint key instances where the interplay between additive combinatorics and other fields - e.g. ergodic theory and algebraic groups - is particularly fruitful.
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