Most Hitchin representations are strongly dense

Hitchin表示的有理逼近

Rational approximation for Hitchin representations

本文针对亏格至少为3的闭曲面，用动力系统方法证明了Hitchin表示在SL(n,Q)中稠密，并推广到Sp(2k,Q)和G2(Q)等群，获得新结果。

Hitchin表示的一般性质

Generic Properties of Hitchin Representations

本文研究了一般Hitchin表示的性质，证明了其Jordan投影集合与极大阿贝尔子代数中的任意超平面不相交，并以此推导出一般orbifold Hitchin表示具有强稠密性。

非均匀晶格中的Zariski稠密表面群

Zariski-dense surface groups in non-uniform lattices of split real Lie groups

本文研究了非均匀晶格中通过算术方法构造的薄Hitchin表示，证明了在某些条件下这些表示在映射类群作用下形成无限多个轨道。

Strongly dense free subgroups of semisimple algebraic groups II

It was shown in Part I that there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are either cyclic or Zariski-dense. Here we show that the same is true for as long as the transcendence degree of the field is at least $1$ in characteristic zero and at least $2$ in positive characteristic. We also consider related questions for surface groups.

Strongly dense free subgroups of semisimple algebraic groups

We show that (with one possible exception) there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are either cyclic or Zariski dense. As a consequence, we get new generating results for finite simple groups of Lie type and a strengthening of a theorem of Borel related to the Hausdorff-Banach-Tarski paradox. In a sequel to this paper, we use this result to also establish uniform expansion properties for random Cayley graphs over finite simple groups of Lie type.

Submaximal properties in (strongly) topological gyrogroups

A space $X$ is submaximal if any dense subset of $X$ is open. In this paper, we prove that every submaximal topological gyrogroup of non-measurable cardinality is strongly $σ$-discrete. Moreover, we prove that every submaximal strongly topological gyrogroup of non-measurable cardinality is hereditarily paracompact.