11 problems

Let $X$ be a Seifert manifold with base $S^2$, and let $(l,\underline{n}')\in\mathcal I_2^b$. Suppose that there do not exist elements $g_1,\ldots,g_n\in\operatorname{SU}(2)$ satis…

Lattice-point correspondence conjecture. The quantity $D-\gamma(\vec{p})$ coincides with the number of lattice points $\vec{\ell}$ satisfying

Consider Chern--Simons theory on four-fibered Seifert manifolds and the associated boundary-crossing method for resurgent continuation across the Chern--Simons natural boundary. Bo…

Let $\Phi_p^{[j]}(q)^\vee$ be the vector of mock modular forms dual under $q \to 1/q$ to the linear combination of false theta functions $\Phi^{[j]}_p(q)$ associated to the…

Let $M=M\left(b,g;\frac{p_1}{r_1},\ldots,\frac{p_d}{r_d}\right)$ be the orientable Seifert fibration over $\Sigma_g$ of degree $b$ with singular-fiber data…

Homological modularity conjecture. The category $\mathsf{RFC}(\mathfrak{sl}(N),M_3)$ is modular if and only if

Seifert-gauge invariance conjecture. The relative fusion categories $\mathsf{RFC}(\mathfrak{sl}(N),M_3)$ and $\mathsf{RFC}(\mathfrak{sl}(N),M'_3)$ have the same modular data.

Finite-set correspondence conjecture. The connected components of the anyonic $SL(N,\mathbb C)$ flat-connection space are in one-to-one correspondence with the points of

Completeness conjecture. The construction may provide a comprehensive list of modular tensor categories.

Modularity conjecture. The resulting fusion category is modular whenever

The geometric Seifert conjecture. The orientable geometric real components of orientable real unir ruled varieties of dimension $3$ are exactly the orientable Seifert manifolds.