Green-Tao theorem in sparse primes

About two decades ago, Green introduced the transference principle, which provides a powerful framework for studying additive patterns in sparse arithmetic sets. Although recent breakthroughs by Bloom–Sisask and Kelley–Meka establish the presence of 3-APs in the primes without relying on transference, the principle remains a valuable tool for exploring general additive patterns in sparse sets. In this talk, I will take "finding k-APs in primes" as an example to illustrate both the analytic and combinatorial approaches that implement these ideas. No background in higher-order Fourier analysis will be assumed. This talk is based on joint work with Joni Teräväinen.