一、报告题目

Vinogradov's three primes theorem with primes from special sets I, II, III

二、报告人

邵煊程（University of Kentucky ）

三、报告摘要

In 2008 Green and Tao proved that there exist arbitrarily long arithmetic progressions in primes. In doing so they introduced methods from additive combinatorics, namely the "transference principle", to tackle analytic problems involving primes. The main goal of this series of lectures is to explain what the transference principle is, and how it can be adapted to different problems. More specifically we will discuss:

1. Roth's theorem, and the Fourier-analytic transference principle to find 3-term arithmetic progressions in primes;

2. Szemeredi's theorem, and the higher-order version of the Fourier-analytic transference principle to find k-term arithmetic progressions in primes, for any k>3.

3. The transference principle approach to find solutions to the equation N=a_1+a_2+a_3 with a_1,a_2,a_3 coming from a given set A, for example a subset of primes.

4. Applicationsto the case when A is the set of "almost twim primes", and a set of primes in short intervals.

5. Other applications.

四、报告时间和地点

2019年5月7日（星期二）9:30-11:30知新楼B座1032报告厅

2019年5月8日（星期三）19:00-21:00知新楼B座1044报告厅

2019年5月9日（星期四）15:30-17:30 知新楼B座1044报告厅

五、邀请人

赵立璐教授