Generalized Kontsevich Matrix Model (GKMM) with a certain given potential is the partition function of $r$-spin intersection numbers. We represent this GKMM in terms of fermions and expand it in terms of the Schur polynomials by boson-fermion correspondence, and link it with a Hurwitz partition function and a Hodge partition by operators in a $\widehat{GL}(\infty)$ group. Then, from a $W_{1+\infty}$ constraint of the partition function of $r$-spin intersection numbers, we get a $W_{1+\infty}$ constraint for the Hodge partition function. The $W_{1+\infty}$ constraint completely determines the Schur polynomials expansion of the Hodge partition function.
On Calabi-Yau Complete Intersections in Toric Varieties
研究了$d$维环面Fano簇中$r$半样本因子的Calabi-Yau完全交$V$的Hodge理论性质.我们的主要目的是证明第二作者提出的组合对偶与镜像对称预言的Hodge数的对偶是一致的。预计对任意维度奇异卡-丘变体$V$的镜像对称预测的完整验证需要考虑所谓的{ \em弦理论霍奇数} $h^{p,q}_{\rm st}(V)$。我们仅限于弦理论霍奇数$h^{0,q}_{\rm st}(V)$和$h^{1,q}_{\rm st}(V)$ $(0 \leq q \leq d-r) which coincide with the usual Hodge numbers $ h^{0，q}（\widehat{V}）$ and $ h^{1，q}（\widehat{V}）$ of a $ MPCP $-desingularization $ \widehat{V} $ of $ V$。
Triple Hodge integrals and constant Poisson brackets for rank-one Dubrovin-Zhang hierarchies
Korteweg–de Vriesinstituut voor Wiskunde, Universiteit van Amsterdam（阿姆斯特丹大学科特韦格-德弗里斯数学研究所）；Université Bourgogne Europe, CNRS, IMB UMR 5584（勃艮第欧洲大学，法国国家科学研究中心，IMB UMR 5584）
