### Brian Cook

SPECIAL MATHEMATICS COLLOQUIUM
In the 1930's, L.K. Hua extended the work of Vinogradov on the ternary Goldbach conjecture, now known as Vinogradov's Theorem, to give an analogue of the result of Hilbert which is set in the primes. For example, Hua has shown that every sufficiently large integer is the sum of at most nine squares of primes. The main purpose of this talk is to discuss some recent work, joint with T. Anderson, K. Hughes, and A. Kumchev, on an ergodic analogue of the work of Hua. The focus shall be mostly on the case of squares, and here the main ingredient is an analogue of the discrete spherical maximal theorem of Magyar, Stein, and Wainger. |