10 problems

Derivative conjecture. The representation $\rho_1(\tau)$ is $(rk,1)$. If $F$ is non-archimedean, then for every $c>1$ the highest derivative of $\rho_c(\tau)$ is

Factorization conjecture. The composite $\iota_2\circ\iota_1$ factors through $\iota_3$.

Generalized injectivity conjecture. Let $\pi\in\mathrm{Irr}_{\rho}$ and let $\mathfrak n\in\mathrm{Mult}_{\rho}$ be minimal to $\pi$. Set

For $k\geq1$, define … and let $\mathcal{S}_k$ be the corresponding computable subsets, with … … Second- and third-derivative completeness conjecture. One has … The paper proves fi…

Let $sigma, sigma' in \mathrm{Irr}^{square}$ and let $pi in \mathrm{Irr}$. A triple $(sigma,sigma',pi)$ is pre-RdLi-commutative when it satisfies the pre-RdLi-commutativity conditi…

Let $\x03be$ be a probability measure compactly supported in $\x1d53d$, let $P_n=\x220f_{i=1}^n(x-\x03be_i)$ have roots independently sampled according to $\x03be$, and let…

Let $f$ be a polynomial of degree at least $2$ with root set $\mathcal{R}$ and no repeated roots. For each root $r\in\mathcal{R}$, write $f^{(k)}(r)$ for the $k$th derivative evalu…

Let $K$ be a knot with a slice disk $Delta$, and let $J$ be a derivative associated to $Delta$. Levine's prediction. The answer to Question 1 should be that $J$ is itself a slice k…

Let $K$ be a knot, let $J$ be a derivative associated to an $(n+1)$-solution for $K$, where $n$ is a non-negative integer or half-integer, and let $Delta_K(t)$ denote the Alexander…

Let $\mathcal{DP}$ denote the set of Pompeiu derivatives, and let an algebra of functions be called algebrable if it contains an infinitely generated subalgebra. Non-algebrability…