10 problems

Let $T\subset(\mathbb{C}^*)^3$ be the rank-two torus preserving the Calabi–Yau three-form $dx\wedge dy\wedge dz$. Let $\mathcal{H}_{\mathbb{A}^3}^{\operatorname{crit},T}$ be the co…

Let $X$ be a quasiprojective $3$-Calabi–Yau variety. Let $\operatorname{W}^+(X)$ be the algebra generated by symbols $T_m^+(\lambda)$, with $m\in\mathbb{N}$ and…

Let $Q$ be a symmetric quiver with potential $\mathsf{W}$. Let $\mathfrak{g}_{Q,\mathsf{W}}$ be the Lie superalgebra defined from the classical $R$-matrix, and write … The positive…

Spherical shuffle realization conjecture. The homomorphism $\xi$ can be promoted to an algebra isomorphism

Let $Q$ be the three-loop quiver obtained from $Q_r$ by removing the framing vertex and all arrows containing it. For framing vector $\mathbf f=1$ and stability parameter…

Let $Q=(I,\Omega)$ be a doubled quiver, let $\gamma$ be a dimension vector, and let $\mu:M_{\gamma}\to \mathfrak{g}_{\gamma}^{0}$ be the moment map. For a generic regular semisimpl…

Let $\Sigma_g$ be a genus-$g$ surface, let $\mathcal{H}^{\operatorname{\mathfrak{P}}}_{Q_{\Sigma_g},W_{\Sigma_g}}$ be the associated CoHA, and let…

Let $\Sigma_g$ be a genus-$g$ topological Riemann surface, let $\operatorname{Rep}^{\zeta_m}_m(\Sigma_g)$ be the twisted $m$-dimensional representation variety defined by the relat…

Yangian conjecture. The critical CoHA of $(\widetilde{Q},W_Q)$ is isomorphic to the Yangian $\mathcal{Y}_Q$ associated with $Q$:

Let $(Q,W)$ be a symmetric quiver with potential, let $\mathcal{C}$ be a category equipped with the structures assumed in the construction of the CoHA $\mathcal{H}_{Q,W}$, and supp…