Maintaining research-related information in an organized manner can be challenging for a researcher. In this paper, we envision personal research knowledge graphs (PRKGs) as a means to represent structured information about the research activities of a researcher. PRKGs can be used to power intelligent personal assistants, and personalize various applications. We explore what entities and relations could be potentially included in a PRKG, how to extract them from various sources, and how to share a PRKG within a research group.