Abstract: The Virasoro conjecture is a concept in enumerative geometry. It states that the generating function for the Gromov–Witten invariants of a smooth projective variety is annihilated by an action of half of the Virasoro algebra. In this talk, we will first introduce a wall-crossing formula that converts heavy markings to light markings. Then, we will prove that the Virasoro conjecture for Fano complete intersections with only ambient insertions is equivalent to the Virasoro conjecture with only one ambient insertion. In the end, we will prove the Virasoro conjecture for one ambient insertion using wall crossing formula and the twisted theory. This is a work in progress with Qingsheng Zhang and Yang Zhou.