9 problems

Let $B$ be a connected $3$-coloured graph with $2n$ vertices, and consider the quartic rank-three tensor model. Equal leading cumulants conjecture. The supplied source span begins…

Let $M_1,\ldots,M_q$ be melonic, connected $3$-coloured graphs, with $q\in\mathbb{Z}_{>0}$. Define … For each $i$, let $p_i$ satisfy $2p_i=\#V(M_i)$. Strong conjecture. … The right…

Let $B$ be a connected $3$-coloured graph. For $q\in\mathbb{Z}_{>0}$ and $i_1,\ldots,i_q\in\{1,2,3\}$, define … where $V_i$ denotes the quartic pillow invariant of colour $i$, and…

Consider the non-random theories described in the preceding conjecture and the factor graphs associated with them. Subleading-corrections conjecture. In such theories, the correcti…

Let $C_{ij}(t)$ denote the commutator quantity studied in the paper, and consider its expansion in powers of $1/N$. Resummability conjecture. The true $1/N$ expansion of…

Let $r$ be the tensor rank, and restrict the rank-$r$ tensors to an irreducible subspace. Consider a complete $(r+1)$-valent interaction. Higher-rank extension conjecture. The cons…

Let $k\geq 3$, set $m=k-1$, and let $Z_k(\lambda,N)$ and $F_k(\lambda,N)$ denote the partition function and free energy for the positive matrix interaction of order $k$. The paper…

Airy universality conjecture. In any Chern–Simons–matter theory which displays the $N^{3/2}$ behavior for the strict large-$N$ limit of its partition function, the leading term of…

Hidden eigenvector dynamics conjecture. The hidden dynamics of eigenvectors discovered by the authors and described for the Gaussian non-Hermitian ensemble is a general feature of…