In-Person Talk 

We show that there exist infinitely many families of Sasaki-Einstein metrics on every odd-dimensional standard sphere of dimension at least 5. We also show that the same result is true for all odd-dimensional exotic spheres that bound parallelizable manifolds. As a consequence, we confirm conjectures of Boyer-Galicki-Kollár and Collins-Székelyhidi. Based on joint work with Taro Sano and Luca Tasin.