Title：Around the ternary Goldbach problem

Speaker：Xuancheng Shao（University of Kentucky ）

Time：2019.5.6  16：00-17：00

Venue:B1044

Abstract：One of the main themes in analytic number theory is to understand the distribution of primes, many of which are still open. For example, the Hardy-Littlewood conjecture predicts the number of solutions to a given linear system of equations in prime variables. Some of its special cases are the twin prime conjecture and the Goldbach conjecture. 

In the past century, analytic number theorists have developed tools and made some progress towards them. For example, Vinogradov in 1937 proved the ternary version of the Goldbach conjecture, that every large odd integer can be written as a sum of three primes. In this talk, I will start with a historical account on known results and the underlying methods, and then describe a few new results related to the ternary Goldbach problem, whose proofs combine classical methods with new ideas from additive combinatorics.

This is based on joint work with Kaisa Matomaki and James Maynard.