6 problems

Mukhin–Varchenko conjecture. Under these representation-theoretic assumptions on $\alpha_1$ and $\alpha_2$, the corresponding $\mathfrak g$-Selberg integral can be expressed as a r…

A KZ equation or dynamical equation is considered whose solutions take values in a one-dimensional space. Gamma-function formula conjecture. If the space of values of such an equat…

Let $[?]$

Mehta–Dyson conjecture. The Gaussian Selberg integral should satisfy

Fix $0<\mu<2$, set $\tau=2/\mu$, and let $S^{(1)}_t(\mu,u,\varepsilon)$ and $S^{(2)}_t(\mu,u,\varepsilon)$ be the smoothed Bourgade–Kuan–Rodgers statistics defined in the paper, wi…

Mukhin–Varchenko conjecture. If the space $\operatorname{Sing}[\lambda+\mu-\sum_{i=1}^n k_i\alpha_i]$ of singular vectors is one-dimensional, then