5 problems

Furstenberg–Bergelson–Leibman conjecture. These averages converge for $\mu$-almost every $x\in X$ as $\min\\{N_1,\ldots,N_k\\}\to\infty$. When $N_1=\cdots=N_k=N$, write the average…

For each prime $l$, let $v_l(t)$ denote the local factor defined from the trace distribution in $\operatorname{GSp}_{2g}(\mathbb{Z}_l)$, with $v_p(t)=1$, and let…

Pointwise convergence and maximal cone multiplier conjecture. The range of $p$ for which

Bellow–Furstenberg conjecture. For $\mu$-almost every $x\in X$, these averages converge as $\min\{M_1,\ldots,M_k\}\to\infty$.

Let $\{n_j:j\ge 1\}$ be a lacunary sequence of integers, meaning that … For a function $f$ on $\mathbb T$, let $S_{n_j}f$ denote its Walsh-Fourier partial sums, and write…