Vertical D4-D2-D0 bound states on K3 fibrations and modularity

伪模性 of 对数 Gromov-Witten 不变量：$\mathbb{P}^2$ 的镜像

Mock modularity of log Gromov--Witten Invariants: the mirror to $\mathbb{P}^2$

本文研究了对数 Gromov-Witten 不变量的生成函数的模性，证明其为 mock 模形式，并建立了与 $\mathbb{P}^2$ 镜像的对应关系。

Scaling Black Holes and Modularity

Scaling black holes are solutions of supergravity with multiple black hole singularities, which can be adiabatically connected to a single center black hole solution. We develop techniques to determine partition functions for such scaling black holes, if each constituent carries a non-vanishing magnetic charge corresponding to a D4-brane in string theory, or equivalently M5-brane in M-theory. For three constituents, we demonstrate that the partition function is a mock modular form of depth two, and we determine the appropriate non-holomorphic completion using generalized error functions. From …

计数几何与模性在双模数K3纤维化三重Calabi-Yau三重展开中

Enumerative geometry and modularity in two-modulus K3-fibered Calabi-Yau threefolds

本文研究了双模数K3纤维化Calabi-Yau三重展开的计数几何与模性，构造了39个Calabi-Yau镜像对，并展示了其模性下的自由能公式。

F理论真空加权胀开上的相交理论

Intersection Theory on Weighted Blowups of F-theory Vacua

本文证明代数簇加权胀开中例外除子类解析函数的推出公式，并用SU(5) Tate模型验证，进而计算消解F₄与Sp(6)奇点的椭圆Calabi-Yau 4-fold垂直相交配对。