Two topics were discussed in particular, both of which are purely algebraic but whose study was motivated by questions in the theory of modular forms. One is a generalization of the classical theory of polynomials and spherical functions (work in collaboration with T. Ibukiyama) and the other is the study of Rankin-Cohen algebras and their analogy with vertex algebras and conformal algebras (work in collaboration with K. Nagatomo). Both topics were already covered in the 2001-2002 lecture, but have developed considerably since then and have now been treated in detail.
Lecture