4 problems

Let $\Gamma$ be a hypergraph with non-negative weights. For every $k\in\mathbb{Z}_{\geq 1}$, let $\omega_k=\omega_k(\Gamma)$ denote the smallest new eigenvalue of the Laplacian…

Let $\Gamma=([n],w)$ be an arbitrary hypergraph with non-negative weights. Let $\mathcal{KMP}_k$ be the discrete KMP process with $k$ indistinguishable particles on $\Gamma$, and l…

Ordered labeled product-chain conjecture. The chains $\mathbf{X}^{\operatorname{ord,lab}}$ and $\mathbf{X}^{\operatorname{ord,lab}}_{\operatorname{prod}}$ exhibit cutoff around the…

Let $m(\beta)$ denote the spontaneous magnetization of the quantum Heisenberg ferromagnet, represented through the interchange process on $[-r,r]^3$ at inverse temperature $\beta$.…