关于凸体的距离函数与辛辛格曼流形

辛自极凸体空间的可收缩性

Contractibility of space of symplectically self-polar convex bodies

本文研究与Mahler猜想、辛外弹球动力学相关的辛自极凸体空间的拓扑，证明该空间具有可收缩性。

Spectral convergence in geometric quantization --- the case of toric symplectic manifolds

In this paper, we show the spectral convergence result of $\overline{\partial}$-Laplacians when $(X,ω)$ is a compact toric symplectic manifold equipped with the natural prequantum line bundle $L$. We consider a family $\{ J_s\}_s$ of $ω$-compatible complex structures tending to the large complex structure limit, and obtain the spectral convergence of $\overline{\partial}$-Laplacians acting on $L^k$.

On the density function on moduli spaces of toric 4-manifolds

The optimal density function assigns to each symplectic toric manifold $M$ a number $0 < d \leq 1$ obtained by considering the ratio between the maximum volume of $M$ which can be filled by symplectically embedded disjoint balls and the total symplectic volume of $M$. In the toric version of this problem, $M$ is toric and the balls need to be embedded respecting the toric action on $M$. The goal of this note is first to give a brief survey of the notion of toric symplectic manifold and the recent constructions of moduli space structure on them, and recall how to define a natural density functi…

辛自极化多面体的最小容量

Symplectically self-polar polytopes of minimal capacity

本文研究了辛自极化凸体的最小容量，并证明了相关下界不可改进，同时进行了体积相关实验和推测。

所有特征线均为平面的凸体

Convex bodies with all characteristics planar

该研究针对辛空间ℝ²ⁿ（n>1）中的光滑强凸体，证明了满足所有特征线或所有外弹子球轨迹为平面这一条件的凸体，均为球的仿射辛映像。

辛极性与马勒猜想

Symplectic polarity and Mahler's conjecture

本文提出辛自极凸体体积的猜想，并证明其等价于马勒猜想，同时给出了辛容量的上下界。