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

Speaker：Xuancheng Shao（University of Kentucky ）

Abstract：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. Applications to the case when A is the set of "almost twim primes", and a set of primes in short intervals.

5. Other applications.

Time/Venue：2019.5.7  9：30-11：30  B1032

2019.5.8  19：00-21：00  B1044

2019.5.9  15：30-17：30  B1044