Randomness and sphere packings in high dimensions

Music City Center 

How can we use randomness to generate dense sphere packings in high dimensions? "How many" sphere packings of a given density are there in high dimensions? We will discuss a probabilistic approach to this problem (joint with Campos, Jenssen and Sahasrabudhe) and connect these results to predictions from statistical physics by Parisi and Zamponi. We will end with a quick summary of yet another probabilistic approach to sphere packing in high dimensions (due to Klartag) and summarize some open problems about the place in randomness in the study of sphere packing.