Firstly, we discuss some results about structures of topological recursion relations on the moduli space of curves. Then motatived by Virasoro conjecture, we propose three conjectures about universal constraints on Hodge integrals. In the end, we prove these conjectures via tautological relations in lower genus.

Speaker's Bio: Wang Xin, Associate Professor at the School of Mathematics, Shandong University, specializes in symplectic geometry and algebraic geometry. His research focuses on the structural problems of Gromov Witten invariants, such as the Virasoro conjecture, universal equations, and curve modular spaces. He is the principal investigator of the National Natural Science Foundation of China's Youth Science Fund and has published multiple articles in renowned mathematical journals such as Trans. AMS, Advances in Math., Commun. Math. Phys.