8 problems

Kadyrov–Kleinbock–Lindenstrauss–Margulis conjecture. For every $h\in[m+n-1,m+n]$, there should exist a sequence of $a$-invariant probability measures $(\mu_k)_{k\geq 1}$ such that

Let $G'$ be a $Q$-group and let $Gamma'$ be an arithmetic lattice of $Q$-rank one. Let $T'$ act on $Gamma' \backslash G'$ by right multiplication by a diagonalizable element of…

Let $q$ be a prime power, let $\Theta(t)\in\mathbb{F}_q(\!(t^{-1})\!)$ be quadratic irrational, and let $P(t)\in\mathbb{F}_q[t]$ be irreducible. For $n,k\in\mathbb{N}$, define … Fu…

Let $P(t)\in\mathbb{F}_q[t]$ be irreducible. For a lattice $\Lambda_0\in\mathcal{L}_2$, let $\mathbb{T}_P(\Lambda_0)$ be its $P(t)$-Hecke tree, and let…

Let $q$ be a prime power, let $P(t)\in\mathbb{F}_q[t]$ be irreducible, and let $\Theta(t)\in\mathbb{F}_q(\!(t^{-1})\!)$ be a quadratic irrational. Write…

Let $\mathbb{F}_q((t^{-1}))^2$ be the ambient plane, and let the sequences of probability measures considered by Shapira, Paulin, and Kemarsky be defined on its space of lattices.…

Rational-ray escape-of-mass conjecture. For any rational $\xi\in\Omega$, the measures $\mu_{x_n^\xi}$ converge to the zero measure.

Generic equidistribution conjecture. For almost every $\xi\in\Omega$, the averages