8 problems

Let $\widetilde{M}(r)$ be the rank-$r$ moduli space, with matrices $(B_1,B_2,I,J)$, and let $\widetilde{M}(r)^{\mathbb{C}^\times}$ be the fixed locus of the $\mathbb{C}^\times$-act…

Let $N$ be the number of states in a solvable multistate Landau-Zener model, and let its scattering matrix describe the transition amplitudes between asymptotic states. A factoriza…

Intertwining-property conjecture. For more general regular scattering functions $S\in\mathcal{S}_0$, the intertwining property holds on these tubes. The construction is known for a…

Consider the case $G=PSU(N)$ with $N_j$ singularities of fundamental weight $\omega_{N-j}$, so that … Let $m_{j,\alpha}$ be the positions of the singularities and define the monic…

Let $H$ be drawn from a random-matrix ensemble, and let its large-$N$ eigenvalue correlation functions belong to a given Dyson universality class. Let $S$ be the scattering matrix…

SDE conjecture. The evolution of the random reduced transfer matrix can be described by a stochastic differential equation in the scaling limit

For $1\leq j<\mathcal L$ and $1\leq d\leq\mathcal D_j$, let $S_{j,d}$ denote the scattering matrix of the $d^{\text{th}}$ particle of type $j$. Let $t_1^{(j-1,d)}(\lambda)$ be the…

Let $S_{{\cal L},d}$ denote the scattering matrix of the $d^{\text{th}}$ particle of type ${\cal L}$, and let $t^{({\cal L})}(\lambda)$ be the transfer matrix acting on…