Uniformity in the Wiener-Wintner theorem for nilsequences
  We prove a uniform extension of the Wiener-Wintner theorem for nilsequences due to Host and Kra and a nilsequence extension of the topological Wiener-Wintner theorem due to Assani. Our argument is based on (vertical) Fourier analysis and a Sobolev embedding theorem. 
Tanja Eisner and Pavel Zorin-Kranich
math.DS