Representations of p-adic Groups

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The principal investigator pursues the representation theory of p-adic groups, centered on the structural theory of the p-adic groups via Bruhat-Tits theory, and the method of restriction on compact open subgroups. Specifically, combining his work on the construction of supercuspidal representations, explicit computations of Bruhat-Tits buildings and refined minimal K-types, the investigator studies refined types, Hecke algebra isomorphisms, and other related topics.The representation theory of p-adic groups, being an amazing theory in its own right, plays a prominent role in number theory and automorphic forms, hence is fundamental to applications of number theory to computing and cryptography. Recently there have been exciting new advances, including the investigator's construction of supercuspidal representations, which was considered most unreachable objects. These advances open up new questions, which is to be pursued in this project.