8 problems

Galashin--Lam's conjecture. Determine the curves $C$ for which

A monotone link is the projection to ${\mathbb R}^2/{\mathbb Z}^2$ of a curve $C$ from $(0,0)$ to $(m,n)$ whose two coordinates are monotone increasing. A curve is convex if it is…

Let $m,n$ be coprime positive integers. Let $\mathcal{H}_{(m,n)}(X;q,t)$ be the Hikita polynomial, let $\Lambda$ be the ring of symmetric functions in $X$, and let…

Let $m,n\in\mathbb{N}$, and consider rectangular Dyck paths from $(0,0)$ to $(m,n)$ that stay above the main diagonal. Let the associated symmetric function be the one related to t…

Let $M$ and $N$ be positive integers, and define … Let $L_{M,N}$ be the symmetric function associated with the $M,N$-path tuples, let $\mathbf{Q}_{m,n}$ be the elliptic Hall algebr…

Let $M$ and $N$ be positive integers, let $k=\gcd(M,N)$, and set $m=M/k$ and $n=N/k$. Let $L_{M,N}$ be the symmetric function defined as the weighted sum over the relevant tuples o…

Let $\mathrm{Sk}(T^2-D^2)$ be the Homflypt skein algebra of the punctured torus, and let $\mathcal{E}_{\sigma,\bar\sigma}$ be the elliptic Hall algebra with generators…

Let $N$ and $k$ be positive integers, and let the elliptic Hall algebra act in its level $N$ representation. In the Uglov limit, consider the conformal algebra…