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초록

Title : Langlands Functoriality Conjecture Functoriality conjecture is one of the central and influential subjects of the present day mathematics. Functoriality is the profound lifting problem formulated by Robert Langlands in the late 1960s in order to establish nonabelian class field theory. I describe the Langlands-Shihidi method, the local and global Langlands conjectures and the converse theorem which are powerful tools for the establishment of functoriality of some important cases, and survey the interesting results related to functoriality conjecture . I also explain various examples of langlands functorial liftings which have been proved by the comparison of trace formulas, a technique introduced by Langlands, Arthur and their collaborators. i discuss new methods to tackle the functoriality conjecture.