8 problems

Unique-norm integral Fourier matrix conjecture. Then

Let $A$ be an abelian group with $A_e\cong\mathbb{Z}_{2^n}\times\mathbb{Z}_2$ for $n\geq2$. Mixed-even-part conjecture. The modular data of the Drinfeld center of the…

Let $A$ be an abelian group with $A_e\cong\mathbb{Z}_{2^{n+1}}$. Cyclic-even-part de-equivariantization conjecture. The modular data of the Drinfeld center of the $\mathbb{Z}_2$-de…

Let $A$ be a finite abelian group of odd order, and let $\mathcal{C}$ be a quadratic category of type $(\mathbb{Z}_2,A,1)$ whose $\operatorname{Vec}_{\mathbb{Z}_2}$ subcategory has…

Let $A$ be an odd finite abelian group and let $G=\mathbb{Z}_{2^n}\times A$ with $n\geq1$. Inverse-involution near-group conjecture. The constructed modular data are the modular da…

Let $A$ be a finite abelian group, let $G=A\times A$, and let $\langle\langle\cdot,\cdot\rangle\rangle$ be a non-degenerate symmetric bicharacter on $A$. Define…

Let $\mathcal{C}$ be a modular category, and let $(S,T)$ be its modular data. Modular-data determination conjecture. The $S$ and $T$ matrices of $\mathcal{C}$ determine it up to ri…

Let a projective congruence datum that is also Galois have exponent $N$ and global dimension $n$. Stronger congruence conjecture. If $n\equiv 2\pmod{4}$, then … and … The conjectur…