8 problems

Let $(X,\f8sigma)$ and $(Y,\f8tau)$ be multivariable dynamical systems, and let ${\mathcal{A}}(X,\sigma)$ and ${\mathcal{A}}(Y,\tau)$ denote their tensor algebras. Piecewise conjug…

Contraction conjecture. The contraction $C_{13}$ induces an isomorphism

Let $T(mathbb R^d)$ be the tensor algebra equipped with the left and right halfshuffle products, and let $\mathcal{I}(\mathbf{PL}^d_{\leq 2})$ denote the ideal associated with piec…

A multivariable dynamical system consists of the dynamical data associated with its tensor algebra, and two such systems are piecewise conjugate when their underlying dynamics are…

Let $k$ be a field of characteristic zero, let $V_d$ be a $k$-vector space of dimension $d$, and let $\Lambda^{S^2}_{V_d}$ be the graded vector space introduced as a generalization…

Let $k$ be a field of characteristic zero, let $V_d$ be a $k$-vector space of dimension $d$, and let $\Lambda^{S^r}_{V_d}$ be the graded quotient constructed from…

Let $k$ be a field of characteristic zero, let $V_d$ be a $k$-vector space of dimension $d$, and let $\Lambda^{S^3}_{V_d}$ be the graded vector space whose degree-$n$ component is…

Let $k$ be a field, let $V_d$ be a $d$-dimensional vector space, and for $n\geq 0$ define … where $\mathcal{T}^{S^2}_{V_d}[n]=V_d^{\otimes \frac{n(n-1)}{2}}$ and…