# Sean Prendiville

## Lecture notes on Fourier analysis in Ramsey theory.

Lecture notes on Fourier analysis in Ramsey theory.

## Research

Research

**Rado's criterion over squares and higher powers****,**with S. Chow and S. Lindqvist (preprint). Video lecture**A transference approach to a Roth-type theorem in the squares****,**with T.D. Browning, IMRN (2017). Video lecture (download)**Four variants of the Fourier-analytic transference principle****,**OJAC (2017).**Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case****,**Discrete Analysis (2017).**Improvements in Birch's theorem on forms in many variables****,**with T.D. Browning, Journal reine angew. Math. (2017). Video lecture**Matrix progressions in multidimensional sets of integers****,**Mathematika (2015).**Near-optimal mean value estimates for multidimensional Weyl sums****,**with S.T. Parsell and T.D. Wooley, Geom. Funct. Anal. (2013).**Solution-free sets for sums of binary forms****,**Proc. Lond. Math. Soc. (2013).

## Teaching

Teaching

**Fourier analysis in Ramsey theory,****Manchester, 2019.****Mathematics 0C1****, Manchester, 2016 & 2017 & 2018.****Topics in Modern Geometry****, Bristol, 2014.****Number Theory and Group Theory****, Bristol, 2012.****Galois Theory****, Bristol, 2012.**

## Songs I've written:

Songs I've written:

## My old band: http://cymbalsmusic.com

My old band: http://cymbalsmusic.com

## A video (made by Dan):

A video (made by Dan):

## What I'm listening to:

What I'm listening to: