界面与量子代数，I：稳定包络

Shuffle products for elliptic stable envelopes of Nakajima varieties

We find an explicit formula that produces inductively the elliptic stable envelopes of an arbitrary Nakajima variety associated to a quiver Q from the ones of those Nakajima varieties whose framing vectors are the fundamental vectors of the quiver Q, i.e. the dimension vectors with just one unitary nonzero entry. The result relies on abelianization of stable envelopes. As an application, we combine our result with Smirnov's formula for the elliptic stable envelopes of the Hilbert scheme of points on the plane to produce the elliptic stable envelopes of the instanton moduli space.

椭圆稳定包络与超环环空间

Elliptic stable envelopes and hypertoric loop spaces

本文建立了超环簇椭圆稳定包络与环空间K理论稳定包络的联系，为椭圆稳定包络的范畴化提供了可能途径。

通过椭圆稳定包络的枚举几何

Enumerative geometry via elliptic stable envelope

本文利用椭圆稳定包络构造 q-差分方程，在例子中与量子差分方程一致，从而将曲线计数与等变椭圆上同调联系起来。

Elliptic stable envelopes and 3d mirror symmetry

In this thesis we discuss various classical problems in enumerative geometry. We are focused on ideas and methods which can be used explicitly for practical computations. Our approach is based on studying the limits of elliptic stable envelopes with shifted equivariant or Kahler variables from elliptic cohomology to K-theory. We prove that for a variety X we can obtain K-theoretic stable envelopes for the variety X^G of the G-fixed points of X, where G is a cyclic group acting on X preserving the symplectic form. We formalize the notion of symplectic duality, also known as 3-dimensional mirror…

蝴蝶结簇稳定包络的存在性与正交性

Existence and orthogonality of stable envelopes for bow varieties

本文综述 A 型蝴蝶结簇的上同调稳定包络，重点证明其存在性与正交性，并以组合化、简化论证支撑显式计算。

通过临界稳定包络发展移位的量子群

Shifted quantum groups via critical stable envelopes

本文通过临界稳定包络构造移位量子群，并将其与临界上同调Hall代数联系起来，扩展了Nakajima有向图变体的结果到临界情形。

稳定包络、涡旋模空间与Verma模

Stable Envelopes, Vortex Moduli Spaces, and Verma Modules

本文显式构造了涡旋模空间的K理论与椭圆稳定包络，将量子差分方程等同于量子Knizhnik-Zamolodchikov方程，并应用于量子q-Langlands对应的分歧版本。

特定非辛簇的椭圆稳定包络与来自贝特/规范对应的超自旋链动力学$R$矩阵

Elliptic Stable Envelopes for Certain Non-Symplectic Varieties and Dynamical $R$-Matrices for Superspin Chains from the Bethe/Gauge Correspondence

本研究将椭圆稳定包络理论推广至非辛簇，借助贝特/规范对应，通过三维$\n=2$规范理论的Janus配分函数求解超自旋链的动力学杨-巴克斯特方程，并验证了低维约化结果与已有数学结论一致。

cotangent bundles to Grassmannians的稳定包积分

Integrals of stable envelopes for cotangent bundles to Grassmannians

本文研究了Grassmannians的cotangent bundles上自然torus作用的cohomological稳定包积分，通过equivariant局部化计算其非equivariant极限，并给出整数的组合公式。

椭圆量子环面代数 $U_{t_1,t_2,p}(\mathfrak{gl}_{N,tor})$ 与 $A^{(1)}_{N-1}$ 箭图簇的椭圆稳定包络

Elliptic Quantum Toroidal Algebra $U_{t_1,t_2,p}(\mathfrak{gl}_{N,tor})$ and Elliptic Stable Envelopes for the $A^{(1)}_{N-1}$ Quiver Varieties

本文提出构造椭圆量子环面代数顶点算子的新方法，利用椭圆稳定包络公式，所得算子满足交换关系并构造L-算子，证明其为模的 intertwining 算子。

界面与量子代数，II：雪茄配分函数

Interfaces and Quantum Algebras, II: Cigar Partition Function

本文从物理角度探讨3d $\mathcal{N}=2$规范理论的雪茄配分函数，系统发展其基础，并利用量子场论机制解释其在BPS态、非微扰修正及量子K理论等方面的丰富物理与数学性质。