##### Department of Mathematics,

University of California San Diego

****************************

### Analysis Seminar

## Benjamin Krause

#### Caltech

## Discrete analogues in Harmonic Analysis beyond the Calder\'{o}n-Zygmund paradigm

##### Abstract:

Motivated by questions in pointwise ergodic theory, modern discrete harmonic analysis, as developed by Bourgain, has focused on understanding the oscillation of averaging operators -- or related singular integral operators -- along polynomial curves. In this talk we present the first example of a discrete analogue of polynomially modulated oscillatory singular integrals; this begins to unify the work of Bourgain, Stein, and Stein-Wainger. The argument combines a wide range of techniques from Euclidean harmonic analysis and analytic number theory.

Host: Andrej Zlatos

### October 16, 2018

### 9:45 AM

### AP&M 7321

****************************