16 problems

Kontsevich's invariance conjecture. There should be an isomorphism of algebras

Let $K$ be a knot, let $\mathcal{A}$ be the tensor algebra generated by its binormal chords, and let $\partial$ be the differential defined by counting zero-dimensional moduli spac…

Let $(A,\partial)$ be the differential graded algebra associated to the Legendrian object, let $\mathcal{C}=A/I$ be its characteristic algebra, and let the degree distribution of…

Let $X$ be a homotopy differential graded non-unital algebra, and let $X(1)$ be the underlying chain complex of the associated homotopy semigroup. The construction described in the…

Let $\mathsf{CDGA}^1$ be the full subcategory of connected commutative differential graded algebras, and let … be the augmentation ideal functor. Right-transfer conjecture. There i…

Let $A$ be a commutative ring, $M$ an $A$-algebra, and $P_*$ a differential graded algebra resolution of $M$. Let $\mathcal{D}_A^*(P_*,P_*)$ denote the differential graded algebra…

Let $M^{\bullet,\bullet}=\bigwedge^{\bullet,\bullet}V^*\otimes\operatorname{End}(R)$, let $\alpha\in\mathcal{N}_0\cap\mu^{-1}(\zeta)$, and let…

Let $p$ be the prime appearing in the definition of the DGAs $S_{2n}$, and let $l$ be a positive integer. The E-infinity refinement conjecture. For each $l>0$, the DGA $S_{2p^l-2}$…

Let $A$ and $B$ be differential graded algebras (DGAs), and let $\MU$ denote the complex cobordism spectrum. The MU-algebra equivalence conjecture. There exist DGAs $A$ and $B$ tha…

Let $V^{[*]}$ be a differential graded vertex algebra, and let $R^{[*]}(V^{[*]})$ denote its $C_2$-algebra. A Tate resolution conjecture predicts that there should be a Tate resolu…

Let $\Lambda$ be a Legendrian in a $1$-jet space of any dimension whose front has mild singularities. Let $(\mathcal{A},\partial)$ denote its simplicial DGA, and let the Legendrian…

Let $A$ be a differential graded algebra (dga), let $\omega_A\in A$ be an even-degree element, and define … Assume that $A$ has an $A_\infty$-minimal model with higher operations…

Let $L$ be a link in ${\mathbb R}^3$, let ${\mathcal A}_L$ be its combinatorial knot differential graded algebra, and let $\Lambda_L\subseteq ST^*{\mathbb R}^3$ be the unit conorma…

Let $L$ be a differential graded Lie algebra, with Chevalley–Eilenberg construction … Quillen models describe rational homotopy types by differential graded Lie algebras, while Sul…

Let $p$ be a prime, and let $\mathcal{B}$ be the bigraded differential algebra over $\mathbb{Z}/p^{2}$ that describes the algebra of cohomology operations of order $\leq 2$ up to e…

Let $A$ be a simply connected Gorenstein differential graded algebra of finite type. Write $\operatorname{H}^eA$ and $\operatorname{H}^*A$ for its cohomology in degree $e$ and in a…