38 problems

A two-dimensional $\mathcal{N}=(0,1)$ theory is a quantum field theory with the indicated supersymmetry, and TMFs are the topological modular forms associated with such theories. T…

Let $M$ be a spin manifold with a positive Ricci curvature metric, and let its Witten genus be viewed as an invariant in the appropriate ring of modular forms. Stolz's conjecture.…

Let $f_{\operatorname{Wt}}(z)=\sigma(z;g_2,g_3)$ be the Witten genus exponential, and recall that a formal power series $u+\sum_{n\geq 1}c_n\frac{u^{n+1}}{(n+1)!}$ with coefficient…

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

Ginzburg–Kapranov–Vasserot's conjecture. Every elliptic curve $A$ gives rise to a unique equivariant elliptic cohomology theory, natural in $A$.

The $2$-vector bundles described above define a kind of second-order $K$-theory, called $2K$-theory, represented by a spectrum. Baas–Dundas–Rognes conjecture. They conjectured that…

Hopkins' extension conjecture. The map $\sigma(\mathbf{C})$ should be the restriction to $MU\langle 6\rangle$ of a similar map

Hopkins–Miller's orientation conjecture. The spectrum $TMF$ admits an $MO\langle 8\rangle$ orientation such that, for every elliptic spectrum $(\mathbf{E},C,t)$, the diagram

Orbifold conjecture. An ideal F-theory could be obtained by an orbifolding analogous to the construction in homotopy theory that produces $TMF$ or its connected form $tmf$.

F-theory conjecture. This theory should be related to F-theory compactified on the elliptic curve $E$.

The TMF conjecture. The generalized cohomology theory in which the combined field strength lives should be the theory of topological modular forms, $tmf$.

The IIA partition function admits an elliptic refinement, equivalently obtainable from the M-theory $G_4$ description. An $M2$-brane may intersect an $M5$-brane in a fundamental st…

Global ultracommutative structure conjecture. Equivariant $\operatorname{TMF}$ admits the structure of a global ultracommutative ring.

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…

A sigma orientation assigns, for each compact Lie group $G$ and each virtual representation $V\in \mathbf{R}\mathrm{O}(G)$ equipped with a string structure, an equivalence of $G$-e…

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 $p_1,p_2\in X^H$,

Elliptic cohomological realization conjecture. The representation in Theorem gives the level-$(0,1)$ irreducible representation of $U_{q,\kappa,p}(\mathfrak{gl}_{N,\mathrm{tor}})$…

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…

3D-mirror conjecture. There exists a dual variety $\mathsf{X}^{!}$ such that the twisted elliptic stable envelopes of $\mathsf{X}$ and $\mathsf{X}^{!}$ coincide after this identifi…