10 problems

Let $q$ be the deformation parameter, $t$ the time parameter, and let $\mathcal{D}$ denote the discrete $q$-lattice … Let $\mathcal{D}$ be the matrix Fredholm determinant defined e…

Let $J$ be a jump matrix with factorization $J=\Phi_-^{-1}\Phi_+$, let $\tau_W[J]$ be the Widom determinant, let $\tau_{AB}[J]$ be the corresponding Arinkin–Borodin tau function, a…

Kitaev's determinant conjecture. Under these assumptions, the Fredholm determinant satisfies

Let $H$ be a group, let $h\in H$, and let $D_P$ and $D_{\mathcal P_M}$ be the operators associated with the boundary conditions $P$ and ${\mathcal P}_M$. Let $A$ be the relevant bo…

Let $A$ be the function defining the Zakharov–Shabat reflection coefficient, let … and let $A_s$ be the associated operator, with kernel $K_s=A_s^2$. Consider the Riemann–Hilbert p…

The q-Hahn PushTASEP Fredholm determinant conjecture. For the step initial configuration,

Let $q$ satisfy $0<q<1$, let $x_n(t)$ denote the position of particle $n$ at time $t$, and define … For all $\zeta\in\mathbb{C}\setminus\mathbb{R}_{>0}$, the conjectural Fredholm d…

Assume that $0\leq\operatorname{Re}(z+z')<1$ and $z,z',w,z+z'+w\notin\mathbb{Z}$, as in Proposition. Let $C_L$ be the constant in the small-$s$ asymptotics of the confluent hyperge…

Assume the hypotheses of Proposition. Let $C$ be the constant in the asymptotic expansions of the hypergeometric-kernel determinant $D(t)$ as $t\to1$, and define … where $G$ is the…

Let $I+V$ be the generalized sine-kernel operator (GSK), let $x$ be the large asymptotic parameter, and let $\nu$ denote the parameter whose integer shifts restore the determinant'…