One of the important objects of study in modern number theory is
automorphic representations and their L-functions. An automorphic
representation is a representation of a certain matrix group, normally
known as reductive group, and considered as a vast generalization of
classical modular forms. An automorphic representation further
decomposes into their local counterparts, which are representations of
reductive groups over local fields, in particular p-adic groups. I
have been studying various relations among these representations,
especially by using the theory known as theta correspondence. The
theory of theta correspondence allows one to construct a
representation of one group out of another, and thus to compare
representations of different groups. Using this theory, I have
obtained numerous interesting results in the theory of automorphic
representations and their related themes.