You’ll have to access Kellogg’s memories so just follow the only path and observe the memories presented to you by Amari. After witnessing the last memory, examine the TV to leave the memory lounger. Review the details with her. The quest will be complete immediately if selected the option for Virgil. However, whatever options you choose, the conversation will still end finding the rogue scientist, Virigil. The next quest will become available immediately.
If you have Curie as you companion and you have her companion quest (Emergent Behavior) unlocked, the first task of finding the person that can help her will be completed and you’ll have to bring her to Dr. Amari.