高阶辛群的显式强有界性

A Quasi Curtis-Tits-Phan theorem for the symplectic group

We obtain the symplectic group $\SP(V)$ as the universal completion of an amalgam of low rank subgroups akin to Levi components. We let $\SP(V)$ act flag-transitively on the geometry of maximal rank subspaces of $V$. We show that this geometry and its rank $\ge 3$ residues are simply connected with few exceptions. The main exceptional residue is described in some detail. The amalgamation result is then obtained by applying Tits' lemma. This provides a new way of recognizing the symplectic groups from a small collection of small subgroups.

A Quasi Curtis-Tits-Phan theorem for the symplectic group

We obtain the symplectic group as an amalgam of low rank subgroups akin to Levi components. We do this by having the group act flag-transitively on a new type of geometry and applying Tits' lemma. This provides a new way of recognizing the symplectic groups from a small collection of small subgroups. The geometry consists of all subspaces of maximal rank in a vector space of maximal rank with respect to a symplectic form. The main result holds for fields of size at least 3. We analyze the geometry over the field of size 2 and describe its simply connected cover if different from the geometry.

Bijective PC-maps of the unipotent radical of the Borel subgroup of the classical symplectic group

Every commutator preserving bijection of the unipotent radical $Up(2n, R)$ of the Borel subgroup of the classical symplectic group of rank at least 4 over a field $F$ such that $6F=F$ is shown to be the composition of a standard automorphism of $Up(2n,R)$ and a central map. The latter is a bijection which acts as the right multiplication by a matrix from the center of $Up(2n,F)$.

带边曲面上平坦辛丛的符号的可能取值

On possible values of the signature of flat symplectic bundles over surfaces with boundary

该研究确定了带边曲面上秩2p平坦辛丛符号的所有可能整数值区间，且p=1时可指定边界和乐的椭圆、抛物、双曲类型。

Orthogonal groups in characteristic 2 acting on polytopes of high rank

We show that for all integers $m\geq 2$, and all integers $k\geq 2$, the orthogonal groups $\Orth^{\pm}(2m,\Fk)$ act on abstract regular polytopes of rank $2m$, and the symplectic groups $\Sp(2m,\Fk)$ act on abstract regular polytopes of rank $2m+1$.

光滑四次三维流形自同构群的非辛指数

Non-symplectic Indices of Automorphism Groups of Smooth Cubic Fourfolds

研究具有给定辛自同构群的光滑四次三维流形的全自同构群，通过群论和格论方法限制非辛指数，并分类秩19余不变格的所有可能自同构群对。

辛格点计数与高阶海森堡群的zeta函数

Symplectic lattice counting and zeta functions of higher Heisenberg groups

本文通过发展Hecke理论技术，枚举带有非退化辛形式的有限秩o-格点的子格，推导出任意紧离散赋值环o上所有高阶海森堡李代数的子代数zeta函数的显式公式。