## EVENT DETAILS AND ABSTRACT

**Colloquium**
**Title:** Nilsequences in Additive Combinatorics

**Speaker:** Professor Ben Green

**Speaker Info:** University of Cambridge and IAS

**Brief Description:**

**Special Note**: **Note unusual time**

**Abstract:**

Harmonic analysis has proved to be a very effective tool for
studying additive questions in number theory. There are many problems,
however, for
which harmonic analysis does not provide enough information. For some of
these problems success has been possible by considering, instead of simply
the linear exponentials e^{2 \pi i theta n}, more exotic "harmonics"
called nilsequences. The goal of this talk will be to explain (to a
general mathematical audience) what nilsequences are, why they are needed,
and how they have helped to solve concrete problems concerning primes. In
particular we will outline a proof of an asymptotic for the number of
quadruples p_1 < p_2 < p_3 < p_4 <= N of primes which lie in arithmetic
progression. Joint work with T. Tao.

**Date:** Thursday, November 08, 2007

**Time:** 3:00pm

**Where:** Lunt 105

**Contact Person:** Bryna Kra

**Contact email:** kra@math.northwestern.edu

**Contact Phone:** 847-491-5567

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