A Gauss-Bonnet theorem for constructible sheaves on reductive groups

等特征与混合特征下的抛物型动机赫克范畴

Parahoric motivic Hecke categories in equal and mixed characteristic

该研究针对拟分歧缓分歧约化群的抛物型赫克层，证明其等特征与混合特征版本间的典范幺半等价，推广Bando的相关比较结论，证明结合了仿射格拉斯曼簇与动机近环函子。

分次 Hecke 代数与幂零锥上等变可构造层

Graded Hecke algebras and equivariant constructible sheaves on the nilpotent cone

本文证明几何分次 Hecke 代数可实现为幂零锥上等变半单纯层复形的自同态代数，并将相应等变可构造层导出范畴等价描述为分次 Hecke 代数直和上的 DG 模导出范畴，从而给出其范畴化。

仿射格拉斯曼流形上可构造层的E₃融合-卷积乘积模型

A model for the E3 fusion-convolution product of constructible sheaves on the affine Grassmannian

本文将复简约群球面Hecke范畴的卷积乘积提升为∞范畴中的左t正合E₃-幺半结构，利用Beilinson–Drinfeld格拉斯曼流形等工具完成内蕴自守侧的构造。

On some asymptotic formulas for curves in positive characteristic

We prove some general asymptotic formula for the values of $L$-function of a sequence of constructible $\mathbb Q_l$-sheaves on curves over $\mathbb F_q$ with some good asymptotic properties. We also give the asymptotic formula for the number of points on the stack $\mathrm{Bun}_G$ for asymptotically exact sequence of curves and a split reductive group $G$. In the case of $\mathrm{GL}_n$ we prove that the same formula holds if we take only semistable points in the account.

实群、对称簇与朗兰兹对偶

Real groups, symmetric varieties and Langlands duality

本文为实群的环路空间复对称簇与实仿射 Grassmannian 构建了相对与实 Satake 范畴间的典范等价，揭示了相对与几何 Langlands 纲领的联系，并应用于形式性、交换性猜想及对偶群的等同。