I was invited to give a series of two talks in the Core Model Seminar, an online seminar organized by Ernest Schimmerling and Benjamin Siskind, Carnegie Mellon University.

*A stationary-tower-free proof of Sealing*

Sealing is a generic absoluteness principle for the theory of the universally Baire sets of reals introduced by Woodin. It is deeply connected to the Inner Model Program and plays a prominent role in recent advances in inner model theory. Woodin showed in his famous Sealing Theorem that in the presence of a proper class of Woodin cardinals Sealing holds after collapsing a supercompact cardinal. In the first talk, I will outline the importance of Sealing and discuss a new and stationary-tower-free proof of Woodin’s Sealing Theorem that is based on Sargsyan’s and Trang’s proof of Sealing from iterability. In the second talk, I will outline the proof of an extension of the Sealing Theorem that gives models in which Theta is regular. This is joint work with Grigor Sargsyan.