13 problems

Let $\Pi^{\natural} \subset \Lambda\otimes\mathbb{R}\subset V^{f\natural}_{tw}$ be a $4$-dimensional subspace, and let $\mathsf{Top}_{\Pi^{\natural}}$ be the full subcategory of to…

Let $SO_n$-dagger categories be the higher categories equipped with the oriented tangential structure described in the source, and let disk-like $n$-categories be the structures in…

Let ${\mathsf{Vect}}_{\operatorname{inj}}$ be the category of finite-dimensional real vector spaces and injective linear maps, and let ${\mathsf{AdjCat}}_n$ denote the $(\infty,1)$…

Let $\Pi^{\natural}\subset \Lambda\otimes\mathbb{R}\subset V^{f\natural}_{tw}$ be a four-dimensional subspace, and let $\mathsf{Top}_{\Pi^{\natural}}$ be the full subcategory of to…

Let $(\xi, \mathcal P)$ be a pair consisting of a tangential structure and a characteristic class as in the definition of a characteristic pair, and let $\xi'$ be a tangential stru…

Let $M$ be a manifold with a tangential structure, and let $F$ be an embedded submanifold that is Poincaré dual to a characteristic class of $M$. A characteristic structure is the…

Let $n$ be an integer indexing the topological defects of the two-dimensional square lattice, with positive $n$ corresponding to removing quarters of the lattice and negative $n$ t…

Let $\mathcal{C}$ be a braided fusion category and let $G$ act on $\mathcal{C}$ by braided tensor autoequivalences. For $g\in G$, write $X^g_1$ for the inverse defect associated wi…

Local interaction probability conjecture. The probability of locally observing a particular interaction decreases as the quantity

Defect-line interaction probability conjecture. This probability will typically decrease with increasing magnitude of the topological charge and topological index.

Three-dimensional generalized-orbifold conjecture. On the level of topological field theory, this gauging mechanism is implemented by a three-dimensional analogue of generalized or…

Let $\mathcal E_m^\lambda$ denote the minimum energy in weak homotopy class $H_m$ for coupling parameter $\lambda>0$. All-coupling monotonicity conjecture. For every $\lambda>0$, w…

The $D=4$ Galilei superalgebra is obtained by a nonrelativistic contraction of an extended Poincaré superalgebra, and its additional central charges arise in the supersymmetrizatio…