##### Department of Mathematics,

University of California San Diego

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### Graduate Student Combinatorics Seminar

## Sam Spiro

#### UCSD

## Roth's Theorem

##### Abstract:

Szemeredi's theorem states that every set of integers $A$ with positive density contains an arithmetic progression of length $k$ for any $k\ge 3$. The case $k=3$ was originally proven by Roth. In this talk we go through the proof of Roth's theorem, as well as other related ideas such as Salem sets and Gower's norms.

### April 12, 2019

### 10:00 AM

### AP&M 5402

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