Explicit construction of automorphic forms and its application to number theory and geometry

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As the main progress of the study on the number theory, I have succeeded in providing examples of the Jacquet-Langlands-Shimizu correspondence for automorphic forms on the symplectic group of degree two and its inner forms by some theta lifting construction of the automorphic forms, which is a joint work with Takeo Okazaki. As for the geometric application, I have given a general construction of real-valued automorphic functions on symmetric cones, which contain real hyperbolic spaces of general dimension. The former achievement can be regarded as very few examples of the guiding principle of the theory of automorphic forms, called "Langlands principle of functoriality". For the latter we have in mind a geometric application such as the embedding of an arithmetic quotient of a hyperbolic space into a real affine space and its generalization to symmetric cone.