On the center conjecture for the cyclotomic Hecke algebras and cyclotomic KLR algebras

The center conjecture for the cyclotomic Hecke algebra of type G(r,1,n) asserts that its center consists of symmetric polynomials in its Jucys-Murphy operators and its dimension is independent of the characteristics of the ground field and defining parameters. There are similar conjectures for the cyclotomic KLR algebras. In this talk, I shall report our recent progress on these two conjectures. This talk is based on joint work with Jun Hu.