3 problems

Let $r$-spin curves have moduli spaces $\overline{\mathcal{M}}_{g,n}^{1/r,\mathbf{m}}$, and let $\Psi(\mathbf{t})$ be the potential of the $\mathrm{KdV}_r$ hierarchy. Intersection…

Let $g,n\geq 0$ and let $k$ be a positive odd integer. Let $\mu=(m_1,\ldots,m_n)\in\mathbb{Z}^n\setminus k\mathbb{Z}^n_{\geq 0}$ satisfy … with all entries of $\mu$ even. Let…

Let $(B,\vartheta)$ be a spin curve, let $g,d$ be integers, and let $k_1,\ldots,k_n$ satisfy … Write $\overline{c}_k=\sum_{\mu\ \textup{odd}}\kappa_{k,\mu}\cdot\mu$ for the spin co…