A Survey on The Eisenbud-Green-Harris Conjecture

The Eisenbud-Green-Harris (EGH) conjecture offers a generalization of the famous Macaulay’s theorem about the Hilbert functions of homogeneous ideals in a polynomial ring $K[x_1,\dots ,x_n]$. In this survey paper, we provide a good compilation of results on the EGH conjecture that have been obtained so far. We discuss these results in terms of their approaches.