超凯勒流形族中的Picard数--对R.博尔彻兹湖Katzarkov，T. Pantev，N. I.谢泼德-巴伦

Katzarkov-Kontsevich-Pantev猜想在Fano三维簇上的验证

Katzarkov-Kontsevich-Pantev Conjecture for Fano threefolds

本文验证了光滑Fano三维簇的Landau-Ginzburg模型满足Katzarkov-Kontsevich-Pantev猜想。

极小伴随轨道的Katzarkov-Kontsevich-Pantev猜想

Katzarkov-Kontsevich-Pantev conjecture for minimal adjoint orbits

本文证明了极小半单伴随轨道的LG模型满足关于新Hodge理论不变量的Katzarkov-Kontsevich-Pantev猜想。

Landau-Ginzburg Hodge numbers for mirrors of del Pezzo surfaces

We consider the conjectures from the paper by Katzarkov, Kontsevich, and Pantev about Landau-Ginzburg Hodge numbers associated to tamely compactifiable Landau-Ginzburg models. We test these conjectures in case of dimension two, verifying some and giving a counterexample to the other.

Frenkel-Gross连接的不规则Hodge数

Irregular Hodge numbers of Frenkel--Gross connections

本文研究了Frenkel-Gross连接的不规则Hodge数，并证明了关于极小齐次空间镜像Landau-Ginzburg模型的猜想。

Complete curves in the moduli space of polarized K3 surfaces and hyper-Kähler manifolds

Building on an idea of Borcherds, Katzarkov, Pantev, and Shepherd-Barron (who treated the case $e=14$), we prove that the moduli space of polarized K3 surfaces of degree $2e$ contains complete curves for all $e\geq 62$ and for some sporadic lower values of $e$ (starting at $14$). We also construct complete curves in the moduli spaces of polarized hyper-Kähler manifolds of $\mathrm{K3}^{[n]}$-type or $\mathrm{Kum}_n$-type for all $n\ge 1$ and polarizations of various degrees and divisibilities.

对数∂∂̄引理及其若干几何应用（附录与 Rao 共同撰写）

Logarithmic $\bf{\partial\bar\partial}$-lemma and several geometric applications (with an Appendix joint with Sheng Rao)

本文证明了紧致凯勒流形上的对数∂∂̄引理，并扩展了关于谱序列退化和变形的若干几何应用。