Title: Ideals and Determinacy

Abstract: We present some new results regarding the equiconsistency of strong ideals and strong determinacy theories. Ideals and determinacy are two foundational frameworks in set theory and these results give the bi-interpretability between one framework and the other (up to a certain complexity). In particular, one of our theorems answers a variation of a well-known conjecture by Woodin and completes a major research direction in descriptive inner model theory that started by R. Ketchersid in his thesis some 20 years ago. We will give background and history that lead up to these results as well as future research along this direction. This is joint work with G. Sargsyan and T. Wilson.