局部域上秩1李群格的尖点

On the profinite rigidity of lattices in higher rank Lie groups

We investigate which higher rank simple Lie groups admit profinitely but not abstractly commensurable lattices. We show that no such examples exist for the complex forms of type $E_8$, $F_4$, and $G_2$. In contrast, there are arbitrarily many such examples in all other higher rank Lie groups, except possibly $\mathrm{SL}_{2n+1}(\mathbb{R})$, $\mathrm{SL}_{2n+1}(\mathbb{C})$, $\mathrm{SL}_n(\mathbb{H})$, or groups of type $E_6$.

尖点正表示的高阶局部混合

Higher-rank local mixing for cusped positive representations

该研究针对含抛物元的富克斯群的扎里斯基稠密正表示，证明了其商空间上Bowen–Margulis–Sullivan测度的定量局部混合，推导了相关渐近结果，还推广至满足外围根平衡条件的阿诺斯表示。

The sparsity of character tables of high rank groups of Lie type

In the high rank limit, the fraction of non-zero character table entries of finite simple groups of Lie type goes to zero.

Non left-orderability of lattices in higher rank semi-simple Lie groups

We prove that an irreducible lattice in a real semi-simple Lie group of real rank at least two and finite center is not left-orderable.

连通紧李群的2-秩

The 2-ranks of connected compact Lie groups

紧李群$G$的2-秩是$G$的初等2-子群${\mathbb Z}_{2}\times... {\mathbb Z}_{2}$的最大可能秩。紧李群的2-秩（和任何素数$p$的$p$ -秩）的研究始于1953年，由A. Borel和J. - P. Serre。紧李群的2-秩一直是许多数学家研究的对象。紧李群的2-秩与数学中的几个重要领域密切相关。本文综述了关于紧李群的2-秩的一些重要结果。特别地，我们给出了紧连通单李群$G$的2-秩的完全确定。Y. Chen和T. Nagano in [Un invariant gémetrique riemannien，C. R. Acad. Sci. Paris，295（1982），389- 391]和[A Riemannian geometric invariant and its applications to a problem of Borel and Serre，Trans.Amer.Math.Soc.308（1988），273- 297]。

Saturated Fusion Systems on Sylow $p$-subgroups of Rank $2$ Simple Groups of Lie Type

For any prime $p$ and $S$ a $p$-group isomorphic to a Sylow $p$-subgroup of a rank $2$ simple group of Lie type in characteristic $p$, we determine all saturated fusion systems supported on $S$ up to isomorphism.