9 problems

Non-spin-simple class conjecture. If $N$ has an odd intersection form

Spin-structure classification conjecture. The parity of the spin structure classifies the non-hyperelliptic connected components of the strata of quadratic differentials with presc…

Let $\Delta_1$ be the genus-three spin structure specified in the preceding list, and let $Sp(6,\mathbf Z_2)$ act on genus-three spin structures. Consider the generators…

Let $X$ be a simply connected surface and let a sufficiently ample linear system on $X$ have smooth member $E$ of genus $g$. When the adjoint data determine an $r$-spin structure o…

Let $a$ be fixed, and suppose that $r$ is even and $a$ is odd. Let $W_g^\pm(a,r)$ denote the refinement of Witten's class according to spin parity, and let…

Let $k\geq 2$, and let $Q_\delta(1,3,\ldots,2k{-}1\mid2,4,\ldots,2k)$, $Z_{2m}(a_1,\ldots,a_{2m})$, and $\mathcal{L}_\delta$ denote the cyclic-product and building-block quantities…

Let $M^d$ be an orientable spacetime manifold, and let $Z^\text{top}(M^d)$ denote the volume-independent partition function of a local bosonic model. A model has an emergent fermio…

Let $(a_1,\ldots,a_n)$ be a partition of $2g-2$ with non-negative parts. For sufficiently large $r$, let $\mathcal{W}_{g; a_1, \dots, a_n}(r)=r^{g-1}W^r_{g,n}(a_1, \dots, a_n)$ be…

Properness conjecture. For every smooth embedding $\imath:T^p\hookrightarrow\mathbb{R}^{p+2}$, the subgroup ${\mathscr{E}}_{\mathtt{Top}}(\imath)$ is proper in…