6 problems

Let $\mathfrak{g}$ be a simple Lie algebra, let $P$ be its weight lattice and $Q$ its root lattice, and let $Q_{\mathfrak{g}}^N:P/Q\to\mathbb{C}^\times$ be the quadratic form defin…

Let $V$ be a rational, $C_2$-cofinite vertex operator algebra, and let $coverline{\mathcal{C}_V}$ denote its modular tensor category equipped with the reverse braiding. Realization…

Let $\mathcal{C}$ be a braided semigroupal polyadic category with an $n$-ary tensor product, an $n$-ary associator $\scalebox{1.15}{\textsf{\upshape A}}^{\left(2n-1\right)\otimes}$…

Let $\mathrm{A}\boldsymbol{\mathrm{Link}}^+$ be the category of consistently oriented annular links and cobordisms, and let $K^b(\mathrm{A}\boldsymbol{\mathrm{Foam}}^+)$ be the hom…

Braided equivalence conjecture. For $\beta=e^{-\pi i d/8}$, the functor $F$ is a $\mathbb{C}$-linear braided monoidal equivalence. This conjecture identifies the representation cat…

For a completely rational conformal net $\mathcal{A}$, write $\operatorname{Rep}(\mathcal{A})^{\mathrm{rev}}$ for the unitary modular tensor category obtained by replacing its brai…