8 problems

Let $\mathcal{M}_{d,2}^{\rm{LS}}$ be the Zariski closure of the set of second signature matrices of landscape paths in $\mathbb R^d$, and let…

Let $k$ denote the level in the signature construction, and let the theorem referred to as the main result assert the stated dimension result for signature matrices of membranes. A…

A signature tensor is the tensor obtained by evaluating the signature construction at an arbitrary level, generalizing the signature matrices of membranes. All-signature-tensor con…

Uniqueness conjecture. For the dictionaries considered, the solution $X$ is unique among real matrices when

Let $\mathcal{B}_{d,\leq n,r}$ denote the expected signature variety of mixtures of $r$ Brownian motions in dimension $d$, truncated at degree $n$. Algebraic identifiability conjec…

Let $\mathcal{B}_{d,\leq n}$ be the expected signature variety and $\mathcal{N}_{d,\leq n}$ the Gaussian moment variety, with the birational map between them given by the natural l…

Let $\mathcal{P}_{d,k,m}$ and $\mathcal{L}_{d,k,m}$ denote the polynomial and piecewise-linear signature varieties, and let $M$ be the stabilization constant from the preceding cor…

Let $\lambda_{d,k}$ and the bounds in … for all integers $d,m\geq 2$. If true, this determines the thresholds at which the signature varieties stabilize and yields the formula for…