13 problems

Stiénon–Xu conjecture. For every transitive Courant algebroid, there is an isomorphism between its standard cohomology and its naive cohomology.

A Lie algebroid on a manifold is given, and one considers a proposed construction that produces a Lie algebroid on its loop space. A Dirac structure is the relevant Lie algebroid i…

Let $\mathcal E_{\mathrm{twist}}$ be the Courant algebroid associated to the twist, and let the extended BPS complex be the complex for $G=U(5)\times SO(10+k)$ associated to the co…

Let the Courant contact model be the local $L_\infty$-algebra construction associated to the relevant Courant algebroid, and let the cubic model be the constrained-field model intr…

Let $\mathcal E_{\mathrm{twist}}$ be the Courant algebroid over the Dolbeault complex associated to a twist datum. The Costello–Li twist of type I supergravity is the perturbative…

Let $E$ be the Courant algebroid underlying a twisted supergravity background, and let $L\subset E\otimes\mathbb C$ be the involutive isotropic subbundle determined by that backgro…

$L_{\infty}$-algebra conjecture. There exists an $L_{\infty}$ structure on the complex $({\bf F}^{\bullet}_{{\bf b}^-},\mathcal{Q})$, such that its bilinear operation is the symmet…

Choice-independence conjecture. There exists an isomorphism of derived Poisson algebras of degree $(-2)$

Let $E$) be a Courant algebroid and let $L\subset E$ be a Dirac structure admitting a Lagrangian complement $L'\subset E$. A Poissonization functor for Dirac structures assigns a s…

A Beltrami-Courant differential determines a corresponding $L_{\infty}$ subalgebra and its generalized Maurer–Cartan equation. Generalized Maurer–Cartan conjecture. The generalized…

Lagrangianity conjecture. The sub-$2$-groupoid $\mathfrak{L}_{\mathcal{D}}$ is Lagrangian everywhere in $\mathrm{LWX}(M)$.

Let $X$ and $\hat{X}$ be orientifold T-dual spaces equipped with the relevant twists, and let $H^{i,\alpha,H}_\epsilon(X)$ denote the twisted cohomology associated to the involutio…

Let $E$ be a Courant algebroid and let … be the natural homomorphism from naive cohomology to standard cohomology. Conjecture. When $E$ is a transitive Courant algebroid, $\phi$ is…