27 problems

Stolz–Teichner conjecture. The degree-$n$ topological modular forms of $X$ are

Let $G$ be a finite group, let $\mathscr{M}_G$ denote the space of admissible functions on $G$ up to rescaling, and let $\Delta_G\subset\mathscr{M}_G$ be the locus of lattice system…

Let $V^\bullet[\cdot]$ be a topological vertex operator algebra (TVOA), with dot product and bracket product defined by the vertex-operator operations above. The homotopy Gerstenha…

Let $V$ be a topological vertex operator algebra, and let an appropriate topological completion mean the completion of $V$ required in the cited construction. A genus-zero topologi…

A topological vertex operator algebra is the algebraic structure considered in the paper, and a homotopy Gerstenhaber algebra is the corresponding higher-algebraic structure introd…

Eguchi–Hori–Xiong conjecture. The partition function satisfies

Floer-theoretic string topology operations conjecture. For every marked chord diagram $\Gamma$, there is an umkehr map

Let $\mathbb{L}_{SO}^\otimes$ be the proposed oriented $\infty$-operad, and let $\Omega^2\operatorname{Bord}_3^{SO}$ be the symmetric monoidal $\infty$-category of oriented 3-dimen…

Expected properties of Yang–Mills plus Chern–Simons theory. The following assertions are expected: (1) the Lagrangian determines a family of Wick-rotated field theories; (2) the si…

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 $\tilde\beta$ be the bosonic-shadow theory and $\tilde\alpha$ the corresponding fermionic anomaly theory, with a conjectural defect $\tilde z_c$ relating them. Invertibility-tr…

Let $G$ be a fermionic symmetry acting on a super modular tensor category, with anomaly $\tilde\alpha$. Let $F_{\tilde\alpha}$ be the Dijkgraaf–Witten-type theory obtained by summi…

Let $\mathcal{C}$ be a symmetric monoidal $(\infty,n)$-category with duals. A framed extended $n$-dimensional TFT valued in $\mathcal{C}$ is a symmetric monoidal functor from the f…

Fix integers $n\geq 2$ and $k\geq n$, set $q=e^{i\pi/k}$, and let $\mathcal C^{(n,k)}$ be the coherent sheaf of dg categories of line operators of $\mathcal T_{n,k}^A$ over…

Let $n$ be a nonnegative integer, let $\mathcal{S}$ denote the ambient symmetric monoidal category of spaces, and let $\mathcal{A}\in\operatorname{Alg}_n(\mathcal{S})$ be an $E_n$-…

Let $d\geq 0$. Consider the homotopy actions of the relevant orthogonal groups on the indicated higher categories of vector spaces. Framing-action triviality conjecture. The homoto…

Let $(X,W)$ be a B-type open-closed topological Landau-Ginzburg theory, with $X$ a non-compact Calabi–Yau manifold and $W$ a holomorphic function whose critical set $Z_W$ is compac…

Let $H_n$ be the symmetry group in dimension $n$, let $MTH$ be the Thom spectrum associated to this symmetry, and let $I\mathbb Z$ denote the Anderson dual of the sphere spectrum.…

The field $bb R$ has an absolute Galois group whose categorification is related to the extension of real vector spaces by complex super vector spaces. The paper proposes an infinit…

Let $\mathcal C$ be a fusion category over an algebraically closed field of characteristic zero. A $Spin(3)$ homotopy fixed point structure on $\mathcal C$ is the additional struct…

Let $\mathcal C$ be a pivotal fusion category over a field of characteristic zero. An $SO(2)$ homotopy fixed point structure on $\mathcal C$ is the additional structure correspondi…

Bulk-boundary deformation conjecture. Such a mathematical pairing should realize a bulk-boundary operator product expansion under deformation of the BRST operator, and mathematical…

Let $\mathcal A$ be an associative algebra equipped with a differential … For a theory with a single D-brane, the deformation data are encoded by $(\mathcal A,Q)$, and their equiva…

Let $Y$ be the complex manifold under consideration. Write $T^*_fY$ for its formal holomorphic cotangent neighborhood, and let $\beta$ be an inhomogeneous $(0,q)$-form with odd $q$…

Let $F'$ be the dimensional reduction of a 1-2-3 theory $F$, and let $K$ denote $K$-theory, viewed as an $E^{\infty}$ ring spectrum. K-theoretic refinement conjecture. The dimensio…