Novel phases in critical metallic systems with multipolar local moments

I will provide a broad overview of recent theoretical and experimental developments in multipolar systems, emphasizing the new challenges posed by multipolar critical and ordered states of quantum matter. These novel quantum materials involve itinerant electrons, interacting and entangling with multipolar local moments, often on frustrated lattices. We discuss the novel phases that may arise from such interactions, especially when conduction electron system possesses a large spin-orbit coupling. Theoretical models for Pr₂Ir₂O₇ and PrV₂Al₂₀ will be considered as concrete examples for discussion.