We present some ideas involved in the proof of the equiconsistency
of AD_\reals + Theta is regular and the existence of a strong,
pseudo-homogeneous ideal on P_{\omega_1}(\reals). Some variations of this
hypothesis are also shown to be equiconsistent with AD_\reals + Theta is
regular. This work is related to and partially answers a long-standing
conjecture of Woodin regarding the equiconsistency of AD_\reals + Theta is
regular and CH + the nonstationary ideal on \omega_1 is \omega_1-dense. We
put this result in a broader context of the general program of understanding
connections between canonical models of large cardinals, models of
determinacy, and strong forcing axioms (e.g. PFA, MM). This is joint work with G. Sargsyan and T. Wilson.