12 problems

Let $\mathcal{C}$ be a symmetric monoidal $(\infty,n)$-category with duals. A framed extended $n$-dimensional TFT valued in $\mathcal{C}$ is a symmetric monoidal functor from the f…

Ferrer’s conjecture. Any such $\mathcal{C}$ admits an $\operatorname{O(n)}$-volutive structure that restricts on $\mathcal{C}^\times$ to the canonical $\operatorname{O(n)}$-action…

Let ${\mathsf{RigidCat}}_n$ denote the category of rigid symmetric monoidal $n$-categories, let $O_n$ act on it through the action supplied by the adjoint-category conjecture, and…

Let ${\cal C}$ be a symmetric monoidal $(\infty,n)$-category that is fully dualisable, with every $k$-morphism satisfying the condition stated in the source for $1\leq k\leq n-1$.…

Let $d\geq 0$. Consider the homotopy actions of the relevant orthogonal groups on the indicated higher categories of vector spaces. Framing-action triviality conjecture. The homoto…

The two-dimensional Ising model has a low-energy effective field theory, and a field theory is topological if its observables depend only on the relevant topological data rather th…

Let $SO(2)$ act on the symmetric monoidal bicategory $\mathbb{F}_{cfd}$ of framed two-dimensional bordisms with fully dualizable objects. Write $(\mathbb{F}_{cfd})_{SO(2)}$ for the…

Let $\mathbb{F}_{cfd}$ be the symmetric monoidal bicategory of framed two-dimensional bordisms with fully dualizable objects, let $\mathcal{C}$ be a symmetric monoidal bicategory,…

Let ${\textup{Bord}}^{\textup{fr}}_{n}$ be the framed bordism $n$-category, let $\mathcal{C}$ be a symmetric monoidal $n$-category, and let an $n$-dimensional extended TQFT be a sy…

The oriented two-dimensional bordism bicategory $\mathbb{B}ord_{2}^{or}$ is the source for oriented two-dimensional topological field theories, and a fully dualizable object is an…

Let $m\geq 0$, and let ${\rm Bord}^{G}(n)$ denote the symmetric monoidal bordism $(\infty,n)$-category with $G$-structure. Let $(m+n)\text{-}\mathrm{Vect}$ be the symmetric monoida…

Let $\mathscr{C}$ be a symmetric monoidal infinity $n$-category. A fully dualizable object of $\mathscr{C}$ is an object satisfying the dualizability conditions at every categorica…