7 problems

Let $M$ and $M'$ carry homogeneous bihamiltonian structures … For small open subsets $U\subset M$ and $U'\subset M'$, let ${\cal B}_{U}$ and ${\cal B}_{U'}$ be the corresponding we…

Let $\mathcal W$ be a web, and let its abelian relations mean the relations among the defining foliations obtained by summing closed one-forms along the leaves. A Liouvillian exten…

Let $\boldsymbol{\mathcal W}$ be a 6-web satisfying the five listed properties: it is linearizable and skew, has maximal 2-rank equal to $10$, has 1-rank at least $5$, and has a 5-…

Let $n\geq 2$ be even, let $\Pi_n$ be the index set used in the source, and let $AR_\nu(\boldsymbol{\mathcal E}_n)$ be the abelian relation associated with $\nu\in\Pi_n$. Abelian-r…

Let $n\geq 2$ be even, and let $\boldsymbol{\mathcal W}_{0,n+3}$ be the web by rational curves induced by the forgetful maps on $\mathcal M_{0,n+3}$. Burau's conjecture. The web…

Legendrian Gronwall conjecture. Every Legendrian 3-web admits at most one distinct local linearization in $\mathbb{P}^3$, except when it is locally equivalent to the dual 3-web of…

Let $\mathcal W$ and $\mathcal W'$ be germs of linear $3$-webs on $(\mathbb C^2,0)$ with non-vanishing curvature, and let $\varphi:(\mathbb C^2,0)\to(\mathbb C^2,0)$ be a germ of b…