14 problems

Let $P$ be a framed partial $2$-monoid, and let $|D_\Sigma^2(\mathbb{R}^{\infty};P)_\bullet|$ denote the space of $2$-dimensional discs with configurations in $\mathbb{R}^{\infty}$…

Integration conjecture. For every such $\Sigma$ and $A$, there is an equivalence

Let $R$ be a $C_n$-ring spectrum. The twisted Dennis trace is a map … Horev's identification gives … where $\int_{S^1_{\mathrm{rot}}} R$ is the $C_n$-equivariant factorization homo…

Let $C$ be a premodular category and let $\Sigma$ be a $2$-fold. Define the additive category $cy_{\Sigma}(C)$ whose objects are collections of $C$-colored points and tangent vecto…

Invertibility conjecture. The algebra $\mathcal{A}$ is invertible if, and only if, it is $(n+1)$-dualizable and the canonical maps

Let $n$ be a nonnegative integer, let $\mathcal{S}$ denote the ambient symmetric monoidal category of spaces, and let $\mathcal{A}\in\operatorname{Alg}_n(\mathcal{S})$ be an $E_n$-…

A smooth constructible $G$-fiber bundle is a smooth constructible $G$-equivariant fiber bundle between equivariantly framed $\mathcal{O}_G$-manifolds with boundary. Equivariant pus…

Let $\boldsymbol{\mathrm{KhR}}_N$ be the braided monoidal 2-category with duals obtained from Khovanov–Rozansky homology, and let the sweep-around property denote the property disc…

Skein-theoretic cobordism conjecture. We further conjecture that $F_M$ is given on $X$ and $Y$ by

Let $n\geq 0$. Write $\operatorname{{\sf Cat}}_n^{\operatorname{{\sf adj}}}$ for the full $\infty$-subcategory of $(\infty,n)$-categories in which every $k$-morphism, for $0<k<n$,…

Let $DG_t$ be the symmetric monoidal $cinfty$-category of $\mathbb{C}$-linear presentable stable dg categories equipped with accessible t-structures compatible with filtered colimi…

Let $cmathcal{A}$ be a braided tensor category, and let the constructions of Li-Bland and Ševera and of the paper be applied to the associated surface data. Agreement conjecture. T…

Let $\mathcal{C}$ be a symmetric monoidal $(\infty,1)$-category and let $\mathfrak{Alg}_{n}(\mathcal{C})$ be the symmetric monoidal $(\infty,n+1)$-category of…

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