5 problems

Consider discrete curves in $\mathbb{C}^2$ reduced to arclength-parametrized curves by setting $g_k=1$ for all $k$. Let the flow directions be determined by … Here $Q_k$ are the cr…

Let $\mathcal J$ and $\hat{\mathcal J}$ be the ideals defining the quotient algebras $\mathcal A_{\mathcal J}$ and $\mathcal A_{\hat{\mathcal J}}$, and let $\partial_{t_\ell}$,…

Hierarchy-identification conjecture. The topological deformation of the Principal Hierarchy is related to the $q$-deformed KdV hierarchy and the Volterra hierarchy through these La…

Let $p,q,r e 0$ satisfy the local Calabi–Yau condition $1/p+1/q+1/r=0$, with $r=-pq/(p+q)$. Set $sj=-(2j-2)!(p^{2j-1}+q^{2j-1}+r^{2j-1})$, $alpha=p/sqrt{p+q}$, and…

The generating function of cubic Hodge integrals satisfying the local Calabi–Yau condition is the generating function under consideration for the hierarchy. Fractional Volterra hie…