Video Lectures

Many data analysis pipelines are adaptive: the choice of which analysis to run next depends on the outcome of previous analyses. Common examples include variable selection for regression problems and hyper-parameter optimization in large-scale...

Sums of Dirichlet characters ?n?x?(n)?n?x?(n) (where ?? is a character modulo some prime rr, say) are one of the best studied objects in analytic number theory. Their size is the subject of numerous results and conjectures, such as the Pólya...

Approximations of infinite groups

Goulnara Arzhantseva

We discuss various (still open) questions on approximations of finitely generated groups, focusing on finite-dimensional approximations such as residual finiteness and soficity. We survey our results on the existence, stability and quantification of...