Graph Integrals on K\"ahler Manifolds

报告人：颜俊榕（美国东北大学）

时  间：2026年7月15日14:30

地  点：海韵园实验楼S106

内容摘要:

Graph integrals arise in quantum field theory and encode particle interactions. They also play important roles in mathematics, including knot theory, mirror symmetry, and enumerative algebraic geometry. Their rigorous definition is subtle, however, since the corresponding integrands are often singular and not Lebesgue integrable.

In joint work with Minghao Wang, we prove a convergence result for Feynman graph integrals on closed real-analytic K\"ahler manifolds. Using Getzler's rescaling technique, we show that the graph integrands extend to the Fulton--MacPherson compactification as differential forms with mild divisorial-type singularities, which allows us to define the integrals rigorously as Cauchy principal value integrals. As an application, we construct the higher-genus B-model invariants on Calabi--Yau threefolds predicted by Bershadsky--Cecotti--Ooguri--Vafa. Through mirror symmetry, these invariants are expected to correspond to higher-genus Gromov--Witten invariants, which are notoriously difficult to compute directly.

个人简介：

颜俊榕，博士，毕业于加州大学圣芭芭拉分校，师从戴先哲教授。目前在美国东北大学（波士顿）从事博士后研究工作。主要研究方向为谱理论、整体微分几何以及数学物理中的相关问题。相关工作发表在JIMJ, Math. Z.和JGP上。

联系人：贺飞