As an observer of Kellogg's memories, you can watch the dream play out, interact with the people or find the continuation to skip the memory. The final memory of a child and an individual from The Institute is the one you're looking for.
Access the television in the final memory to leave the memory sequence. Speak with Doctor Amari to learn about an old scientist from the Institute and leave the Memory Den. You can speak to Nick Valentine here for more insight into him.