**Title**: Uniform distribution of polynomial and non-polynomial sequences in nilmanifolds

**Speaker**: Florian Richter (Northwestern University)

**Abstract**: The notion of uniform distribution conceptualizes the idea of a sequence of points that disperses evenly and proportionately throughout all parts of a mathematical space. The topic of my talk is the uniform distribution of a variety of polynomial and non-polynomial sequences in nilmanifolds, which are differentiable manifolds that possess a transitive nilpotent Lie group of diffeomorphisms. Our main results in this direction generalize the work of Leibman on the uniform distribution of polynomial orbits in nilmanifolds and the work of Frantzikinakis on the uniform distribution of nil-orbits along functions from a Hardy field. This also connects to open questions in arithmetic combinatorics and, in particular, to generalizations of Szemeredi’s theorem.