I am invited to give a talk on Nov 12, 2021, in the Cross-Alps Logic Seminar, an online seminar organized by the logic groups of Udine, Turin, Genoa and Lausanne.

*Large Cardinals and Determinacy*

Determinacy assumptions, large cardinal axioms, and their consequences are widely used and have many fruitful implications in set theory and even in other areas of mathematics. Many applications, in particular, proofs of consistency strength lower bounds, exploit the interplay of determinacy axioms, large cardinals, and inner models. I will survey some recent results in this flourishing area. This, in particular, includes results on connecting the determinacy of longer games to canonical inner models with many Woodin cardinals, a new lower bound for a combinatorial statement about infinite trees, as well as an application of determinacy answering a question in general topology.