K3曲面的Joyce不变量和模拟θ函数

The level structure in quantum K-theory and mock theta functions

This is the first in a sequence of papers to develop the theory of levels in quantum K-theory and study its applications. Our main results in this paper are toric mirror theorems for permutation-equivariant quantum K-theory with level structure. In some of the simplest examples, we see the surprising appearance of Ramanujan's mock theta functions.

多重 D3-瞬子与模拟模形式 II

Multiple D3-instantons and mock modular forms II

本文证明了在 Calabi-Yau 三流形紧化的 type IIB 弦理论中，DT 不变量生成函数为向量值模拟模形式这一条件在双瞬子阶的充分性，通过引入新 theta 级数族并构造保持全纯接触结构的 SL(2,Z) 作用来实现。

The $u$-plane integral, mock modularity and enumerative geometry

We revisit the low-energy effective $U(1)$ action of topologically twisted $\mathcal N=2$ SYM theory with gauge group of rank one on a generic oriented smooth 4-manifold $X$ with nontrivial fundamental group. After including a specific new set of $\mathcal Q$-exact operators to the known action, we express the integrand of the path integral of the low-energy $U(1)$ theory as an anti-holomorphic derivative. This allows us to use the theory of mock modular forms and indefinite theta functions for the explicit evaluation of correlation functions of the theory, including but not restricted to thos…

卡拉比-丘三维流形的模伪性

Mock modularity of Calabi-Yau threefolds

本研究针对IIA型弦论卡拉比-丘紧化中D4-D2-D0 BPS指标的生成函数所满足的模反常方程，提出用不定θ级数求解任意荷情形的方法，可通过有限个傅里叶系数确定生成函数对应的模形式。

A Theta lift representation for the Kawazumi-Zhang and Faltings invariants of genus-two Riemann surfaces

The Kawazumi-Zhang invariant $φ$ for compact genus-two Riemann surfaces was recently shown to be a eigenmode of the Laplacian on the Siegel upper half-plane, away from the separating degeneration divisor. Using this fact and the known behavior of $φ$ in the non-separating degeneration limit, it is shown that $φ$ is equal to the Theta lift of the unique (up to normalization) weak Jacobi form of weight $-2$. This identification provides the complete Fourier-Jacobi expansion of $φ$ near the non-separating node, gives full control on the asymptotics of $φ$ in the various degeneration limits, and p…