The so-called Strong Chang's Conjecture $(\aleph_3,\aleph_2) \twoheadrightarrow (\aleph_2,\aleph_1)$ is generally believed to be a very strong property possibly approaching the strength of a huge cardinal. Unfortunately, inner model theory so far has failed in corrobariting this intuition. In the first part of this talk we will give a quick overview of the state of the art and furthermore try to elucidate the problems that have blocked progress so far.
In the second part we will introduce what we call the Long Chang's Conjecture which is simply a Chang's conjecture involving infinitely many cardinals. We will then explain how this Long Chang's Conjecture allows us to side-step aforementioned problems and achieve Projective Determinacy. Of particular interest in this argument is the way we achieve mouse reflection in the context of the core model induction. An approach we believe will also be useful when considering the more traditional forms of Chang conjectures.