7 problems

Kontsevich–Witten hypergeometricity conjecture. The Kontsevich–Witten tau-function is also a hypergeometric solution of the BKP hierarchy.

Generalized BGW hypergeometricity conjecture. The generalized BGW tau-function, after a simple rescaling of times, is a hypergeometric solution of the BKP hierarchy.

Let $\operatorname{DP}$ be the set of strict partitions, and let a hypergeometric BKP tau-function be expressed as … with $r_\lambda=e^{\sum_{j=1}^{\ell(\lambda)}\xi(\lambda_j)}$.…

Let $\operatorname{DP}$ be the set of strict partitions. A hypergeometric BKP tau-function has the form … where $r_\lambda=\prod_{j=1}^{\ell(\lambda)}\prod_{m=1}^{\lambda_j}r(m)$ f…

Let $\operatorname{DP}$ denote the set of strict partitions, let $Q_\lambda({\bf t})$ be the normalized Schur Q-function, and let $\delta_{k,j}$ denote the specialization with valu…

BKP identification conjecture. The BKP hierarchy can be identified with the restriction of the odd-times flows of the KP hierarchy to this locus.

Hirota-equation conjecture. $Z(t_1,\beta;z)$ is a solution of a Hirota equation that is differential with respect to $t_1$ and difference with respect to $\beta$. The conjecture pr…