标题： 通过椭圆稳定包的枚举几何 显示英文标题

标题： Enumerative geometry via elliptic stable envelope

摘要： 假设$X$是一个椭圆稳定包存在的代数簇。 在本文中，我们从$X$的椭圆稳定包构造自然的$q$-差分方程。 在例子中，这些方程与量子差分方程一致，这给出了$X$的 Dubrovin 联络的自然$q$-形变。 量子差分方程的解提供了计数$X$中曲线的生成函数。 通过这种方式，我们的构造将曲线计数与等变椭圆上同调联系起来。 这是一篇基于作者在第16届MSJ-SI：椭圆可积系统、表示论与超几何函数研讨会，东京2023年演讲的综述论文。 显示英文摘要

摘要： Assume $X$ is a variety for which the elliptic stable envelope exists. In this note we construct natural $q$-difference equations from the elliptic stable envelope of $X$. In examples, these equations coincide with the quantum difference equations, which give a natural $q$-deformation of the Dubrovin connection of $X$. Solutions of the quantum difference equations provide generating functions counting curves in $X$. In this way, our construction connects curve counting and equivariant elliptic cohomology. This is an overview paper based on the author's talk at the workshop The 16th MSJ-SI: Elliptic Integrable Systems, Representation Theory and Hypergeometric Functions, Tokyo 2023.