Title: Exotic Lagrangian tori in Grassmannians Show Chinese title

Title: 奇异的拉格朗日环面在格拉斯曼流形中

Abstract: We describe an iterative construction of Lagrangian tori in the complex Grassmannian $\operatorname{Gr}(k,n)$, based on the cluster algebra structure of the coordinate ring of a mirror Landau-Ginzburg model proposed by Marsh-Rietsch. Each torus comes with a Laurent polynomial, and local systems controlled by the $k$-variables Schur polynomials at the $n$-th roots of unity. We use this data to give examples of monotone Lagrangian tori that are neither displaceable nor Hamiltonian isotopic to each other, and that support nonzero objects in different summands of the spectral decomposition of the Fukaya category over $\mathbb{C}$. Show Chinese abstract

Abstract: 我们描述了在复数Grassmannian$\operatorname{Gr}(k,n)$中拉格朗日环面的迭代构造，该构造基于Marsh-Rietsch提出的镜像Landau-Ginzburg模型的坐标环的簇代数结构。 每个环面都带有Laurent多项式，并由$k$-变量的Schur多项式在$n$-次单位根处控制。 我们利用这些数据给出了一些单调拉格朗日环面的例子，这些环面既不可分离，也不与彼此哈密顿同伦，且在Fukaya范畴在$\mathbb{C}$上的谱分解的不同分量中支持非零对象。