5 problems

Universal-profile conjecture. The profiles computed for self-avoiding walk and branched polymers on the complete graph should also apply to the corresponding SR and LR models at an…

Branched-polymer universality conjecture. The real model also lies in the universality class of branched polymers.

Let ${\mathcal A}=\{H_1,\ldots,H_N\}$ be the hyperplane arrangement with $H_i=\{\mathbf{x}\in\mathbb C^r\mid h_i(\mathbf{x})=0\}$. Define $T_{\mathcal A}\subset\mathbb R_{>0}^N$ by…

Let ${\mathcal A}=\{H_1,\ldots,H_N\}$ be a hyperplane arrangement in $\mathbb C^r$, let $C_{\mathcal A}$ be its complement, and let $CP_{\mathcal A}$ be the associated space of con…

Let ${\mathcal A}$ be a central hyperplane arrangement, and let $CP_{\mathcal A}$ denote its space of connected branched polymers. The Orlik–Solomon algebra is the algebra associat…