My main research areas are (i) ergodic theory and (ii) metric number theory. In ergodic theory, I am interested in characterization problems of invariant measures and also some problems of infinite measure preserving ergodic transformations. In metric number theory, I am interested in ergodic and probabilistic properties of transformations associated with continued fractions and related number expansions. The research on ergodic transformations with infinite invariant measure connects those two subjects.