Unsolved Problems

Let $K \subset \mathbb{R}^N$ be a balanced compact set with normalized Gaussian measure $\gamma_\infty(K) \geq 0.99$. Does $10K$ contain a compact con...

Is every set $\Lambda \subset \mathbb{Z}$ either a Sidon set, or a set of analyticity?...

Let $\mathcal{F}$ be all integrable functions $f : [0, 1] \to \mathbb{R}_{\geq 0}$ with $\int f = 1$. For $1 < p \leq \infty$, estimate $c_p := \inf_{...

Describe the rough structure of sets $A \subset \mathbb{Z}$ with $|A| = n$ and $\|\hat{1}_A\|_1 \leq K \log n$....

Let $A \subset \mathbb{R}$ be a set of positive measure. Does $A$ contain an affine copy of $\{1, \frac{1}{2}, \frac{1}{4}, \dots\}$?...