The rigidity of the graphs of homology spheres minus one edge

The Hirsch conjecture holds for normal flag complexes

Using an intuition from metric geometry, we prove that any flag and normal simplicial complex satisfies the non-revisiting path conjecture. As a consequence, the diameter of its facet-ridge graph is smaller than the number of vertices minus the dimension, as in the Hirsch conjecture. This proves the Hirsch conjecture for all flag polytopes, and more generally, for all (connected) flag homology manifolds.

同调球面的面数

The face numbers of homology spheres

本文通过构造多面体复形上的应力代数，证明其Gorenstein性和弱Lefschetz性质，从而证明了单纯实同调球面的$g$-猜想。

精确6-割刚性与Dirac k=4问题6-正则情形的小阶超连通性

Exact 6-cut rigidity and small-order superconnectivity for the 6-regular case of Dirac's k=4 problem

针对Dirac提出的k=4未解情形，研究6-正则(4,1)-图的存在性，通过计算和理论分析证明最小顶点数为16、非平凡6-割的岸大小至少为15，并分类了割矩阵。

例外群的极大子群与 Quillen 维数

Maximal subgroups of exceptional groups and Quillen's dimension

本文研究 $p=2$ 时的 Quillen 维数性质，通过极大子群分析与计数论证，证明奇特征 Lie 型例外有限单群的 $2$-扩张除有限例外外均满足该性质，并缩减了 Quillen 猜想极小反例的可能分量。