# Prof. Joris Roos, University of Wisconsin-Madison: "Discrete analogues of maximally modulated oscillatory integrals of Stein-Wainger type"

Jul 05, 2019 from 10:15 AM to 11:15 AM

LMS 4 - Raum 312 - Diskussionsraum

Abstract:

In 2001, Stein and Wainger introduced an interesting class of maximally modulated oscillatory integral operators related to Carleson's theorem. This talk is about the L^{2} theory for discrete analogues of some of these operators. This problem features a number of new and substantial difficulties arising from a curious fusion of number theory and analysis. Our approach is building on work of Krause (2018) and Krause-Lacey (2015). A key ingredient for the proof is a certain multi-frequency L^{2} estimate that also seems interesting in its own right. We will discuss a classical argument of Bourgain that allows us to obtain such an inequality by making use of variation-norm estimates. The required variation-norm estimates in this context were established recently in work of Guo-Roos-Yung (2017).