Ergodic theorems for polynomials in nilpotent groups

Abstract

The principal results proved in this expository thesis are the IP polynomial Szemerédi theorem for nilpotent groups and the multiple term return times theorem with nilsequence weights. It also contains extensions of the convergence theorem for nilpotent polynomial multiple ergodic averages and the return times theorem to locally compact second countable amenable groups.

PhD thesis, University of Amsterdam, xi+146 pages. Based on arXiv:1111.7292, arXiv:1206.0287, arXiv:1208.3977, arXiv:1210.5202, arXiv:1301.1884

References in corpus (2)

• Nilspaces, nilmanifolds and their morphisms
• A nilpotent IP polynomial multiple recurrence theorem

Cited by in corpus (4)

• Some open problems on multiple ergodic averages
• Möbius disjointness for homogeneous dynamics
• Combinatorial properties of Nil-Bohr sets
• Automatic sequences, generalised polynomials, and nilmanifolds