Hecke algebras play important role in the study of algebraic groups, finite groups of Lie type and Lie algebras. The KLR algebras (also named as quiver Hecke algebras) can be regarded as Z-graded analogues of Hecke algebras, which were introduced by Khovanov and Lauda, and by Rouquier, about 12 years ago. There have been considerable progress on the modular representation theory of Hecke algebras since the birth of KLR algebras. In this talk I shall give a survey on these progress with a focus on the theory of the cyclotomic Hecke algebras and cyclotomic KLR algebras of type A.

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