7 problems

Shuffle-of-areas closure conjecture. If all $i_j$ are distinct, then

Let $\operatorname{rcl}$ denote the right-closure operator, and let $\operatorname{im}\operatorname{rcl}$ be its image, the space of right-closure invariants. Let…

Let $\mathsf{ConjInv}$ denote the conjugation invariants in dimension $d=3$, and let a shuffle with letters mean a shuffle product involving letters. The signed volume is the degre…

Let $\mathsf{ConjInv}$ be the algebra of conjugation invariants, and call a homogeneous element a generator at level $n$ if it is one of the homogeneous generators used for this sh…

Let $T(\mathbb{R}^d)$ be the tensor algebra, let $V$ be the space of loop invariants, and let $[V,\mathbb{R}^d]$ and $[T(\mathbb{R}^d),\mathbb{R}^d]$ denote the corresponding commu…

Let $T(\mathbb{R}^d)$ be the tensor algebra, let $S$ denote the shuffle algebra of shuffle products of letters, and let $\mathsf{ConjInv}$ denote the conjugation invariants. Define…

Let $X$ be an integral homology $S^1 \times S^3$ containing an essentially embedded torus $\mathcal{T}$, let $Y_0$ be the cross-section obtained by the associated $0$-surgery, and…