On July 17, 2018 I gave a talk at the 1st Girona conference on inner model theory in Girona.
Long games and Woodin cardinals
Abstract: Itay Neeman proved the determinacy of analytic games of length $\omega \cdot \theta$ for countable $\theta > \omega$ from a sharp for $\theta$ Woodin cardinals. We aim for a converse at successor ordinals and show how to obtain $\omega+1$ Woodin cardinals from the determinacy of analytic games of length $\omega \cdot (\omega+1)$.
This is joint work with Juan P. Aguilera.
Notes for this talk are available here.