6 problems

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

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…

Homotopy shuffle commutativity conjecture. The homotopy shuffle product is homotopy commutative for every such $A^\bullet$. Consequently, the induced product

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…