Information retrieval has long been focusing on connecting people with information they need to complete their tasks. Recently, the meaning of this has changed dramatically as more and more AI agents now consume, retain, and act on information on a user's behalf. Consequently, information management now also takes place \emph{inside} the agent in the form of memory management. In this perspective paper, we argue that \emph{agentic memory management} (AMM), which studies the structure, analysis, organization, storage, searching, retrieval, and \emph{use} of information in an intelligent agent's memory, is a natural extension of IR research and an area in which the IR community can make distinctive contributions. Specifically, we first present a system-level framework for AMM and introduce a computational taxonomy of memory objects as \emph{constants}, \emph{functions}, and \emph{operators}, each with distinct retrieval semantics. Then, we compare AMM with established IR research and identify their difference and connections. Last but not least, we outline a research agenda covering benchmarks, candidate principles of memory utility, optimization procedures that mix parametric and non-parametric updates, and more. We hope this paper could attract more people, both inside and outside the IR communities, to think more about AMM problems and research from IR perspectives.

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