8 problems

Ratio-limit conjecture. One has

Asymptotic linear-bound conjecture. For every $p$ there exists a constant $A_p>0$ such that

Let ${\mathbb F}$ be an algebraically closed field of characteristic $\ell$, let $V={\mathbb F}^{d}$ carry the relevant nondegenerate bilinear form, and let $\mathcal{G}$ be…

Let $V={\mathbb C}^{d}$ with $d>4$, fix the relevant nondegenerate quadratic and, when $d$ is even, symplectic forms, and let $\mathcal{G}$ be one of $GL(V)$, $O(V)$, or $Sp(V)$. F…

Let $p$ be a prime, let $b_n$ denote the sequence of quantities associated with the direct summands of the tensor powers considered in the paper, and let $t_p$ be the exponent from…

Let $G$ be a finite group, let $k$ be a field of characteristic $p$ dividing the order of $G$, and let $M$ be an Omega-algebraic $kG$-module, meaning that the non-projective indeco…

Let $G$ be a finite group, let $k$ be a field of characteristic $p$ dividing the order of $G$, and let $M$ be a finite-dimensional $kG$-module. Let $\phi(n)=\mathsf{c}_n^G(M)$ be t…

Let $G$ be a finite group, let $k$ be a field of characteristic $p$ dividing the order of $G$, and let $M$ be a finite-dimensional $kG$-module. Cosine-value conjecture. If…