25 problems

Full-faithfulness conjecture. The functor associated with the non-formally-completed prestack,

Higher-codimension bulk-to-corner conjecture. One has $\mathcal{I}_n(x,y)=c_nP(x,y)$ for some constant $c_n$. This generalizes the boundary and corner propagator identities to high…

Let $\mathfrak{g}$ be a Lie bialgebra with cobracket $\delta$, let $U(\mathfrak{g})$ denote its universal enveloping algebra, and let $A^{!}_{\mathcal{N}}$ be the $E_1$ Koszul dual…

Let $M$ be a manifold, let $\mathcal{E}$ be an elliptic complex on $M$, and let $P_{\mathcal{E}}$ be its propagator. Consider the corresponding propagator on…

Gaitsgory–Lurie quantum fundamental local equivalence conjecture. The functor $\operatorname{FLE}$ is an equivalence.

Let $M$ be a spacetime, let $g \in [\mathrm{Lor}(M)/\mathrm{Diff}^{+}(M)]$ be an asymptotically flat and stationary black-hole solution, and let $\mathscr{E}_g$ be the differential…

Let $(F,Q,(-,-),W)$ be a free BV field theory, and suppose its Green's witness $W$ is obtained by truncating an $L_{\infty}$ algebra to its underlying cochain complex. Green-witnes…

Let $d4d4_g$ and $d4d4$ denote the linearized conformal-gravity and general-relativity theories, respectively, and let $d4d0\mathrm{bs}^{\mathrm{cl}}(-,d4d4)$ denote their classica…

Eager's conjecture. One can construct quantizations of these theories such that there is an equivalence of 2-dimensional holomorphic factorization algebras

Let $(\mathcal{E},\otimes)$ be a $\mathcal{G}$-monoidal dg category with t-structure, for $\mathcal{G}$ as in the source. This induces an $\mathbb{E}_1$-factorisation cosheaf of ca…

Gaitsgory's factorization conjecture. There exists a fully faithful functor

Let $\mathfrak{d}$ be the cotangent Lie algebra considered in the source, let $Y_1(\mathfrak{d})$ be its Yangian at parameter $1$, and let $\Delta_z$ be its meromorphic coproduct.…

Dhillon's conjecture. At any level $u$, the self-dualities of these factorization module categories arising from the displayed identifications and the self-duality theorem for Whi…

Let $Z$ be the conical manifold and let $\targetcat$ be the target category appearing in the cone decomposition theorem. For each integer $d\geq 0$, consider the restriction functo…

Non-perturbative Noether theorem. If $\cT$ has $X$-symmetry, then there exists a factorizing line bundle $\mc{L}$ on the prefactorization space $X_c$ and a map of prefactorization…

Let $\mathbb{X}$ and $\mathbb{Y}$ be field theories, and let $\mathsf{Obs}_{\mathbb{X}}$ and $\mathsf{Obs}_{\mathbb{Y}}$ denote their observables. For an $\mathbb{E}_n$-algebra $A$…

Let $\mathcal T$ be a Poisson BV theory on $N$, and let $\mathcal Z(\mathcal T)$ be its universal bulk theory. Let … be the respective projections. Write…

Let $G$ be a reductive algebraic group. Let $R_2=H^\bu(\mathbb{A}^2,\mathcal{O}_{\mathbb{A}^2}^{\mathrm{alg}})$, let $\mathfrak{g}$ be the Lie algebra of $G$, and let…

Agreement conjecture. The three different definitions of factorization algebras agree in the special case of locally constant factorization algebras.

Let $\mathcal{M}$ be a Lorentzian spacetime and let the classical observables form a factorization algebra. Epstein–Glaser renormalization provides a framework for constructing qua…

The classical model for the free theory with Green-hyperbolic operator $P$ is a prefactorization algebra on $M$ assigning to each open $U$ the commutative dg algebra…

Let $\mathbb C$ be the configuration-space curve, let $\operatorname{Ran}(\mathbb C)$ be its Ran space, and for $x\in\operatorname{Ran}(\mathbb C)$ let…

Let $\mathcal{C}$ be a nice $\use@mathgroup \M@U \symAMSb{E}_{n}$-monoidal $\infty$-category. Let $\mathfrak{Alg}_{n}^{\textup{FA}}(\mathcal{C})$ denote Scheimbauer’s…

Relative Deligne conjecture. The centralizer is computed by $E_n$-Hochschild cohomology.

Exponential-law conjecture. The functor $\underline{\pi_1}_*$ is an equivalence under rather weak conditions on $X$ and $Y$.