5 problems

Nekrasov–Shatashvili identification conjecture. The $\mathscr{Q}$-top free energy $F_g^{\mathscr{Q}\text{-{\rm top}}}$ coincides with the Nekrasov–Shatashvili effective twisted sup…

Consider the monodromy matrix constructed from the gauge-fixed Lax matrix of the chiral affine Gaudin model. Yang–Baxter monodromy conjecture. There exists a quantisation of this m…

Some non-linear sigma models are classically integrable. Integrability-survival conjecture. The classical integrability of many such models should survive quantisation. This is a b…

Let $\mathfrak{q}$ be the Lie algebra under consideration, let $\nu\in\mathfrak{q}^*_{\rm reg}$, and let $\widetilde{\mathcal{A}}_{\nu}\subset\mathcal{U}(\mathfrak{q})$ be the comm…

Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra, let $\mathcal{S}(\mathfrak{g})^{\mathfrak{g}}$ be its invariant algebra, and let…