The podcast episodes provided discuss several aspects of brain activity, including how it changes during different sleep stages, the neural processes involved in dreaming, and the cognitive benefits associated with certain activities like learning to juggle.

For example, episode "How sleep affects our brains" delves into the changes in brain activity during different sleep stages, such as the synchronized firing of neurons during deep sleep and the paradoxical brain activity during REM sleep. Similarly, episode "Dreams: What Could They Mean?" explores the brain activity and neural processes involved in dreaming.

Additionally, episode "What Are You Doing on Your Cellphone? & The Fascinating World of Paradoxes" mentions research on how learning to juggle can lead to changes in the white matter of the brain, related to various cognitive functions.