in complex algebraic geometry, the decomposition theorem asserts that semisimple geometric objects remain semisimple after taking direct images under proper algebraic maps. this was conjectured by kashiwara and is proved by mochizuki and sabbah in a series of long papers via harmonic analysis and d-modules. in this talk, i would like to explain a simpler proof in the case of semisimple local systems using a more geometric approach. as a byproduct, we recover a weak form of saito's decomposition theorem for variations of hodge structures. \\ \\ joint work in progress with chuanhao wei.