49 problems

Let $X$ be a topological space, let $\nu\in\mathbb{Z}$ be an anomaly coefficient, and consider families parametrized by $X$ of two-dimensional $\mathcal{N}=(0,1)$ supersymmetric qu…

Let $Q\colon\mathbb{Z}^d\to\mathbb{Z}$ be positive definite and unimodular, let $b$ be the corresponding even bilinear form, and let $\Theta_Q=\Theta_b$ be its theta function. Let…

Let $p$ be an odd prime, let $C/\overline{\mathbb{F}}_p$ be a supersingular elliptic curve, and let $Q(\ell)$ be the totalization of the semi-cosimplicial spectrum … Write…

Let $\mathit{tmf}$ denote the connective topological modular forms spectrum, let $\Sigma_3$ be the symmetric group on three letters, and let $\mathit{tmf}^{t\Sigma_3}$ denote its T…

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 $tmf$.

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

Let $X$ be the target of a 3-dimensional $\mathcal{N}=1$ supersymmetric sigma model, and let $X_+$ denote $X$ with a disjoint basepoint. Sigma-model boundary-condition conjecture.…

Let $\mathcal{T}$ be the spectrum assembled from spaces of boundary conditions for two-dimensional theories, with its multiplicative structure induced by stacking. Boundary-theory…

Let $b$ be a symmetric bilinear form and let $\theta_b$ be the holomorphic section of the complex Looijenga line bundle…

Let $\mathcal{Z}$ denote the invariants of closed 3- and 4-manifolds and the proposed maps associated to cobordisms, valued in modules over $\operatorname{TMF}$. TMF-valued TQFT co…

Let $G$ be a symmetry group and fix an anomaly. Equivariant TMF classification conjecture. Two-dimensional minimally supersymmetric quantum field theories with $G$-symmetry and the…

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

Let $Z$ be a 3-dimensional topological or supersymmetric quantum field theory. TMF-module categorification conjecture. There is a $\operatorname{TMF}$-module $M(Z)$ whose underlyin…

Let $b$ be a unimodular positive-definite symmetric bilinear form on $\mathbb{Z}^d$, and let $\mathfrak{d}_b\in \pi_{-2d}\operatorname{TMF}$. Write…

Projection-splitting conjecture. It has been conjectured that this map is only one of many projection maps decomposing $MString$ into a direct sum of variants of $tmf$ and spectra…

Let $G$ be a compact Lie group acting on a manifold $X$, let $X{/{\!/}^{\nabla}}G$ denote the quotient stack encoding the action with connection data, and let…

Segal–Stolz–Teichner conjecture.

Let $A_{-2c}$ be the kernel of … For $c=32,31/2,15,14$, the kernel is respectively isomorphic to $\mathbb{Z}/3,\mathbb{Z}/2,\mathbb{Z}/2,\mathbb{Z}/2$. The kernel-generator conject…

Let $\mathbb{V}$ be a unitary self-dual VOSA of central charge $c=n/2$, equivariant under a finite group $G$ with anomaly…

Let $\mathbb{V}$ be a unitary self-dual VOSA of central charge $c=n/2$ containing the affine Lie VOA $\mathfrak{g}_k$, and let $G$ be the corresponding compact simply-connected gro…

Let $(M_{8\ell+2},g_M^{\mathrm{spin}})$ be a closed differential spin manifold, and let $g_M^{\mathrm{string}}$ be a lift of its spin structure to a differential string structure.…

The VOSA-to-$\operatorname{TMF}$ class conjecture. The VOSA should determine a class

The twisted $E_8$-equivariant lift conjecture. The element $e_8$ lifts to

Let $V$ be a rational vertex operator algebra with central charge $c=24n$, where $n$ is an integer, and suppose that $V$ has only one irreducible module. Let the character of $V$ b…