7 problems

Let $(A,u)$ be a finitely generated quantum group, and let $b_k$ and $p_k$ denote the growth and random-walk quantities constructed in the paper. Here $f_k\approx g_k$ means that t…

Let $L$ be a finitely generated Lie PI-algebra. Write $\gamma_L(n)$ for its growth function, and let $\ln^{(q)}n$ denote the $q$-fold iterated natural logarithm. Intermediate-growt…

Let $F_r$ be a free group and let $w\in F_r$ be a non-primitive element. Let $CA(w)$ denote the set of cyclically reduced automorphic images of $w$. Cyclically reduced orbit growth…

Let $G$ be a connected Lie group. The notions of algebraic and analytic thickness and thinness are those used in the paper, and Theorem is the thick/thin dichotomy for unimodular c…

Let $G\subset U_N^+$ be a compact quantum group, and let $\widehat{G}$ denote its discrete dual. For each $Q\in U_N$, let $\Gamma_Q$ be the associated discrete quantum group. Polyn…

Let $S$ be a left reversible semigroup if any two principal left ideals intersect, and call $S$ finitely generated when a finite subset generates it. Its growth is polynomial when…

Let $G$ be an infinite finitely generated group. The exponential Nielsen growth conjecture asserts that there are an integer $n$ and a generating $n$-tuple $S\in\Gamma_n(G)$ such t…