Vinayak Gupta

Stability of Shifted Complexes via the Second-Moment Defect of the Up-Laplacian

Let $K$ be a finite pure $k$-dimensional simplicial complex, with $k\ge1$, on the vertex set $[n]$ and with facet family $K_k$. Let $\lambda_1(K)\ge\lambda_2(K)\ge\cdots>0$ be the nonzero eigenvalues of its $(k-1)$-dimensional up-Laplacian, and, after ordering the vertices so that $\deg_K(1)\ge\cdots\ge\deg_K(n)$, let...