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The conference will overview the role of representation theory in various disciplines such as automorphic forms, harmonic analysis, and invariant theory developed over the past half a century, present recent progress in this field, and finally aim to extrapolate it into future. The main topics include automorphic forms, invariant theory, representation theory of reductive groups over local fields and related subjects. Professor Howe's work and insights have been most influential in the development of these fields of mathematics and the conference will be an occasion to celebrate his 70th birthday.