Research Interests: Additive Combinatorics, Ergodic Theory, Discrete Fourier Analysis.
This paper we prove that dense subsets of primes must contain a corner configuration using transference principle. This is a different method than the paper below. We hope to generalize our method to give a stronger bound on numbers of corners.
We prove that any dense subsets of prime must contain an affine copies of any finite configurations. We use the hypergraph regurarity method in weighed hypergraph.
Motivated the number theory part in the resulrs above, we use Goldston-Yildirim sieve and circle method to calculated the number of almost prime solutions to system of diophantine equations with rank conditions in the sense of Birch.