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.

报告人简介：王新，山东大学数学学院副教授，研究领域为辛几何、代数几何，主要关注于Gromov-Witten不变量的结构问题，如Virasoro猜想，万有方程与曲线模空间等，主持国家自然科学基金青年科学基金，在Trans. AMS， Advances in Math., Commun. Math. Phys.等著名数学杂志发表文章多篇。