Boundedness of Degree of the basic field of an arithmetic reflection group in Lobachevsky space

Classification of $(1{,}2)$-reflective anisotropic hyperbolic lattices of rank $4$

A hyperbolic lattice is called \textit{$(1{,}2)$-reflective} if its automorphism group is generated by $1$- and $2$-reflections up to finite index. In this paper we prove that the fundamental polyhedron of a $\mathbb{Q}$-arithmetic cocompact reflection group in the three-dimensional Lobachevsky space contains an edge such that the distance between its framing faces is small enough. Using this fact we obtain a classification of $(1{,}2)$-reflective anisotropic hyperbolic lattices of rank $4$.

Strong and uniform boundedness of groups

A group G is called bounded if every conjugation-invariant norm on G has finite diameter. We introduce various strengthenings of this property and investigate them in several classes of groups including semisimple Lie groups, arithmetic groups and linear algebraic groups. We provide applications to Hamiltonian dynamics.

环上定义的单连通分裂 Chevalley 群的强有界性

Strong boundedness of simply connected split Chevalley groups defined over rings

本文研究 S-算术分裂 Chevalley 群的强有界性，证明由共轭类定义的字度量直径仅依赖共轭类数量，并通过正规生成集示例说明界的尖锐性及小型生成集障碍。

正交型一致高阶算术群中的共轭宽度

Conjugacy width in uniform higher rank arithmetic groups of orthogonal type

研究正交型各向异性高阶算术群的共轭宽度，在GRH下证明次数≥17且含非阿基米德赋值时宽度有界，并建立宽度界与同余子群问题的等价联系。