全纯辛结构与C-辛结构的Moser同痕

Calogero-Moser空间的辛全纯密度性质

The symplectic holomorphic density property for Calogero-Moser spaces

本文引入辛全纯密度性质等概念及对应理论，证明n粒子Calogero-Moser空间$\mathcal{C}_n$具有该性质并刻画其全纯辛自同构群，为相关空间的自同构研究提供基础。

The Density Property for Calogero--Moser spaces

We prove the algebraic density property for the Calogero--Moser spaces $\mathcal{C}_{n}$, and give a description of the identity component of the group of holomorphic automorphisms of $\mathcal{C}_{n}$.

The symplectic isotopy problem for rational cuspidal curves

We define a suitably tame class of singular symplectic curves in 4-manifolds, namely those whose singularities are modeled on complex curve singularities. We study the corresponding symplectic isotopy problem, with a focus on rational curves with irreducible singularities (rational cuspidal curves) in the complex projective plane. We prove that every such curve is isotopic to a complex curve in degrees up to 5, and for curves with one singularity whose link is a torus knot. Classification results of symplectic isotopy classes rely on pseudo-holomorphic curves together with a symplectic version…

具有内部自由度的广义Calogero--Moser空间的密度性质

The Density Property for Generalized Calogero--Moser Spaces with Inner Degrees of Freedom

本文证明了具有内部自由度的广义Calogero--Moser空间的密度性质，从而描述了其全纯自同构群，并揭示了其与非交换$\mathbb{R}^4$上$\mathrm{SU}(2)$瞬子模空间的联系。

伪全纯圆盘的存在性：基于非阿基米德圆盘势

Existence of pseudo-holomorphic disks via non-archimedean disk potentials

通过引入非阿基米德解析势函数，证明若分次单调拉格朗日子流形具有非零圆盘势，则其任何光滑同痕中的拉格朗日子流形在任意驯服近复结构下都界一个Maslov指标为2的J-全纯圆盘。

Holomorphic Bundles and Many-Body Systems

We show that spin generalization of elliptic Calogero-Moser system, elliptic extension of Gaudin model and their cousins can be treated as a degenerations of Hitchin systems. Applications to the constructions of integrals of motion, angle-action variables and quantum systems are discussed. Explicit formulas for the Lax operator on the higher genus surfaces are obtained in the Shottky parameterization. The constructions are motivated by the Conformal Field Theory, and their quantum counterpart can be treated as a degeneration of the critical level Knizhnik-Zamolodchikov-Bernard equations.