北京雁栖湖应用数学研究院

马修·伯菲特 , 李京艳 , 吴杰 , 杨南君 , 周嘉伟

Larry So

2025年02月27日 14:30 至 15:30

A3-4-301

Zoom 204 323 0165 (BIMSA)

A toric orbifold $X$ is characterized by a simple polytope $P$ and a characteristic function $\lambda$. A fundamental problem is to understand the relationship between the topology of $X$, the combinatorial data of the pair $(P,\lambda )$, and the algebraic structure of its cohomology $H^{\ast }(X)$.

In this talk, I will present a formula that expresses cup products in the cohomology of a 4-dimensional toric orbifold $X$ in terms of the pair $(P,\lambda )$. Notably, when $X$ is a toric surface, this formula recovers the "dual" of the intersection form from Intersection Theory. In addition, this leads to a criterion for the triviality of Steenrod operations on the cohomology of $X$, which allows us to extract topological information about $X$.

This talk is based on joint work with Xin Fu and Songbaek Song.