101 problems

Non-inner automorphism conjecture. Every finite non-abelian $p$-group has a non-inner automorphism of order $p$.

Let $Y$ be a Calabi–Yau manifold, meaning that $Y$ has trivial canonical bundle and $h^1(\mathcal{O}_Y)=0$. Let $\mathrm{Nef}^+(Y)$ denote the convex hull of the rational points of…

Let $G$ be a reductive group, let $\Out_F(G)$ be its group of $F$-rational outer automorphisms, let $\theta\in\Out_F(G)$, and let $\mathfrak w$ be a Whittaker datum. Outer-automorp…

Slaman–Woodin conjecture. The set

Let $p$ be a prime, let $k$ be an algebraic closure of $\mathbb{F}_p$, let $\Gamma$ be the Galois group of $k/\mathbb{F}_p$, and let $G$ be a finite group. Let…

Berkovich's conjecture. Every finite non-abelian $p$-group admits an automorphism of order $p$ which is not inner.

Let $F_n$ be a free group. A subgroup $H\leqslant F_n$ is auto-fixed if $H=\operatorname{Fix} S$ for some set of automorphisms $S\subseteq \operatorname{Aut}(F_n)$, and it is 1-aut…

Anti-symplectic involution conjecture. Then

Nielsen prevalence conjecture.

Let $F$ be a free group, and associate to each element of $F$ the feature vector of weights of its Whitehead Graph in the corresponding feature space. A region is a bounded subset…

Let $F$ be a free group. For each positive integer $n$, let $U_n$ be the set of all non-minimal elements in $F$ of length $n$, and let $NU_n\subset U_n$ be the subset consisting of…

Let $F$ be a free group, and let a non-minimal element of $F$ be represented by its corresponding Whitehead Graph. A Nielsen automorphism is an automorphism of the type used in Whi…

Kapovich's discreteness conjecture. The set

For each $n,N\geq 1$, let ${\underline{\operatorname{Aut}}}^{\leq N}(A_{n,\mathbb Q})$ and ${\underline{\operatorname{Aut}}}^{\leq N}(P_{n,\mathbb Q})$ denote the filtered automorp…

Tameness Conjecture. The automorphism $f$ can be isotoped so that it preserves the splitting and the induced automorphism $g$ on $H_1$ is train-track generic and has a tame one-dim…

Let $\overrightarrow{u}$ be an autocorrect sequence, and let a $\overrightarrow{u}$-Engel automorphism mean an automorphism satisfying the corresponding Engel condition. Let $G$ be…

Let $\overrightarrow{u}$ be an autocorrect sequence, and let a $\overrightarrow{u}$-Engel automorphism mean an automorphism satisfying the corresponding Engel condition. Consider a…

Let $\alpha\in\operatorname{Aut}(F_k)$ be an iwip automorphism with trivial fixed subgroup, and let $\Gamma$ be the finite bipartite graph whose vertices are the fixed points of th…

Let $X^{an}/K$ be an analytic K3 surface with the lattice $\Lambda_X$, period homomorphism $\rho_X$, valuation vector $v_X:=val_K\circ\rho_X$, and affine piecewise-linear action on…

Let $X$ be a projective variety and let $\sigma$ be a wild automorphism of $X$, meaning that … for every nonempty reduced closed subscheme $Y\subsetneq X$. For an abelian variety…

Let $X$ be a projective variety and let $\tau$ be a wild automorphism of $X$, meaning that … for every nonempty reduced closed subscheme $Y\subsetneq X$. Wild automorphism conjectu…

Medvedev's conjecture. $L$ contains a solvable subring of $m$-bounded derived length whose index is $(p,n,m)$-bounded.

Khukhro's conjecture. $G$ contains a subgroup of $m$-bounded derived length and $(p,n,m)$-bounded index.

Khukhro's conjecture. $G$ contains a subgroup of $m$-bounded nilpotency class and $(p,m)$-bounded index.

Let ${\cal L}_n$ be the simplicial category associated with a theory of weak $n$-categories, and suppose an equivalence with the simplicial category characterized by the paper's pr…