88 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 $\mathcal{C}$ 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…

In the 1990s, Crane and Frenkel considered three-dimensional topological field theories of Witten, Reshetikhin and Turaev and the categorical language emerging in geometric represe…

The intermediate random-matrix ensemble described in the paper arises from $U(N)$ Chern–Simons theory on $S^3$, an interacting topological system exhibiting ergodic-to-nonergodic t…

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…

A bihamiltonian deformation of the genus-zero hierarchy is a deformation encoding the recursion relations among correlators of a two-dimensional topological quantum field theory. D…

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

Let $G$ be a compact Lie group, let $\Sigma$ be a closed surface of genus $g$, and let $\mathfrak{M}$ denote the moduli stack of $G$-bundles on $\Sigma$. Let $\tau$ be an admissibl…

Integrability conjecture. The deformations of noncommutative associative algebras found by S. M. Natanzon and corresponding to open-closed two-dimensional topological field theorie…

Correspondence conjecture. There is a one-to-one correspondence between finite quantum groups and three-dimensional topological field theories satisfying the squeezing property, wi…

Grothendieck's topological Teichmüller tower conjecture. The duplication functor $dupl:RG\to {\cal S}$ is an equivalence of categories.

CSW/TLFT equivalence conjecture. The CSW theory for the general inhomogeneous Lie group $IG$ is equivalent to the TLFT with $H={\bf C}[G]$.

Regular c-graph conjecture. The invariants of closed regular c-graphs are invariants of the $3$-manifolds they define by surgery and, up to a normalization factor, are equal to the…

Let $M$ be a manifold and let $\mathcal{A}$ be the open-string algebra, with Hochschild cohomology $H^*(\operatorname{Hoch}(\mathcal{A}))$, while the closed-string BRST cohomology…

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…

Let $G_f$ be a fermionic group, and let $\mathit{FermGrp}$ denote the relevant $\infty$-category of fermionic groups. With the notation of the symmetric monoidal functor … there sh…

Dubrovin–Zhang uniqueness conjecture. Associated to any semisimple 2d topological field theory, there canonically exists a unique integrable hierarchy of topological type such that…

Consider the coupled system $\overline{\mathcal{T}}_{\text{min}}\times T_{\mathfrak g}$, where $\overline{\mathcal{T}}_{\text{min}}$ is the orientation reversal of the minimal SCFT…

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 $M_3$ be a $3$-manifold, let $G$ be a gauge group, and let $\cH(M_3;G)$ denote the Hilbert space of the topologically twisted four-dimensional $\cN=4$ super--Yang--Mills theory…

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 $Z$ 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 $\mathfrak{h}$ be a boundary Lie algebra with 1-shifted Lie bialgebra structure, and let $\mathfrak{h}^*[-1]$ be its shifted dual boundary condition. Assume that the degree-two…