##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Van Vu

#### UCSD

## Solving the Erdos-Folkman conjecture

##### Abstract:

For a sequence A of integers, S(A) denotes the collection of partial sums of A. About forty years ago, Erdos and Folkman made the following conjecture: Let A be an infinite sequence of integers with density at least $Cn^{1/2}$ (i.e., A contains at least $Cn^{1/2}$ numbers between $1$ and n for every larger n), then S(A) contains an infinite arithmetic progression. Partial results have been obtained by Erdos (1962), Folkman (1966), Hegyvari (2000), Luczak-Schoen (2000). Together with Szemeredi, we have recently proved the conjecture. In this talk, I plan to survey this development.

Host:

### October 30, 2003

### 1:00 PM

### AP&M 7321

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