# Workshop on Additive Combinatorics and Algebraic Connections

## Higher Order Stability and Quadratic Arithmetic Regularity Lemmas

Abstract: We present recent work, joint with J. Wolf, in which we define a natural ternary analogue of the order property, called the functional order properly, and show that subsets of $F_p^n$ without the functional order property admit especially strong quadratic decompositions, in which the error part is constrained by linear structure.

### Date & Time

October 27, 2022 | 2:00pm – 3:00pm

### Location

Simonyi 101 and Remote Access

Caroline Terry

### Speaker Affiliation

Oklahoma State University