turkmath.org

Gromov-Witten invariants have important applications in symplectic geometry and algebraic geometry. The Virasoro conjecture predicts that the generating function of Gromov-Witten invariants for smooth projective varieties is annihilated by a sequence of differential operators which form a half branch of Virasoro algebra. When the manifold is a point, Virasoro conjecture is equivalent to Witten's conjecture which was proved by Kontsevich. This conjecture indicates deep connections between Gromov-Witten theory and integrable systems. In this talk, I will describe the current status of Virasoro conjecture and its applications.