Abstract:The cyclotomic Hecke algebras of type $G(r,1,n)$ (Ariki-Koike algebra) were introduced by Ariki and Koike and independently by Broué and Malle, which include Hecke algebras of types $A$ and $B$ as special cases. They play an important role in modular representation theory of finite groups of Lie type, and are in relation with various significant objects, such as quantum groups and rational Cherednik algebras. It is a long-standing open problem to determine the representation type of blocks of a cyclotomic Hecke algebra. In this talk, we will present some development on this problem. This is a joint work with Xiangyu Qi.