17 problems

Level-$(0,-|\boldsymbol w|)$ geometric action conjecture. The tensor product representation

Level-$(0,-1)$ geometric action conjecture. The representation $\mathcal F^{(0,-1)(k)}_u$ of $U_{t_1,t_2,p}(\mathfrak{gl}_{N,tor})$ is equivalent to an expected level-$(0,-1)$ geom…

Let $\operatorname{Bil}\colon \operatorname{Lat}^{\operatorname{op}}\to\operatorname{AbGroup}\subset\mathrm{PicGrpds}$ be the functor of bilinear forms, and let…

Let ${\mathfrak{X}}$ be the symplectic-resolution object under consideration, and let $\Xi_{{\mathfrak{X}}}$ be the parameter set for elliptic canonical-basis classes. Let Properti…

Elliptic stable-basis duality conjecture. For any $p_1,p_2\in X^H$,

Let $\sigma^8$ be the space of homotopy Hopf manifolds, let $\mathcal L$ and $\mathrm{p}_1$ be the maps appearing in the source, and let $MO\langle 8\rangle$ be the Thom spectrum o…

Numerical-map conjecture. There is a numerical map $N$ which is constant with value $\frac{1}{12}$ on $\sigma^8_{\textrm{Milnor}}$.

Let ${\mathscr{F}}$ be a geometric oriented abelian sheaf over a derived stack $\mathsf{S}$. Write $\operatorname{Sp}_{\mathrm{fin}-\mathrm{gl}}$ for the symmetric monoidal…

Type A quiver-variety action conjecture. There exists an action of the elliptic dynamical quantum supergroup $E_{\hbar,\tau}(\mathfrak g_Q)$ on…

Let $\mathsf{X}=\operatorname{Hilb}^{n}(\mathbb{C}^{2})$, and let $\mathsf{X}^{!}$ denote its 3D-mirror dual. Let $\mathbf{U}(a,z)$ and $\mathbf{L}(a,z)$ be the matrices of twisted…

Let $X$ be a smooth symplectic variety with finite $X^{\mathsf{T}}$, and suppose that the elliptic stable envelope exists. For $4\lambda,\mu\in X^{\mathsf{T}}$, define … Here $a$ a…

Independence conjecture. The series $\mathsf{DT}_{r,k}^{\rm ell}(\mathbb{A}^3,q,t,w;p)$ does not depend on the elliptic parameter $p$.

Let $V^\natural$ be the Moonshine vertex operator algebra, let $\mathbb{M}$ be the Monster group, and let $\alpha^\natural\in H^3(\mathbb{M},U(1))$ be the Moonshine anomaly. Write…

Let $m$ be an integer, and let $P_m(d)$ be the free abelian group generated by the isomorphism classes of irreducible positive-energy representations of the universal central exten…

Let $M$ be a closed string manifold. The Höhn–Stolz conjecture. If $M$ admits a Riemannian metric of positive Ricci curvature, then the Witten genus $W(M)$ vanishes. The conjecture…

Twisted Morava theory differential conjecture. The cohomology class $W_7+[H_7]$ corresponds to a differential in twisted Morava $K$-theory and twisted Morava $E$-theory, where…

Let $X$ be a compact, differentiable, $G$-equivariant spin manifold of dimension $24d$. Assume that $\frac{p_1}{2}(X)=0$ and that … where $\pi$ is the map from $X$ to a point and…