Unsolved Problems

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

Let $d \geq 3$ be an odd integer. Give bounds on $\nu(d)$ such that if $n > \nu(d)$ the following is true: given any homogeneous polynomial $F(\mathbf...

Finding a single solution to a polynomial equation $F(x_1, \dots, x_n) = C$ can be very difficult. What conditions on $A$ ensure that the number of su...

Is every group well-approximated by finite groups?...

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

How many Sudoku puzzles have exactly one solution?...

How many Sudoku puzzles with exactly one solution are minimal (removing any clue creates multiple solutions)?...

What is the maximum number of givens for a minimal Sudoku puzzle?...