Category
Problem Set
Status
Sets with Small Fourier L^1 Norm
Describe the rough structure of sets $A \subset \mathbb{Z}$ with $|A| = n$ and $\|\hat{1}_A\|_1 \leq K \log n$....
Bounds for Homogeneous Polynomial Zeros
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...
Polynomial Solutions in Dense Sets
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...
Sofic Groups
Is every group well-approximated by finite groups?...
Affine Copy of Geometric Series
Let $A \subset \mathbb{R}$ be a set of positive measure. Does $A$ contain an affine copy of $\{1, \frac{1}{2}, \frac{1}{4}, \dots\}$?...
Sudoku: Unique Solution Puzzles
How many Sudoku puzzles have exactly one solution?...
Sudoku: Minimal Puzzles Count
How many Sudoku puzzles with exactly one solution are minimal (removing any clue creates multiple solutions)?...
Maximum Givens in Minimal Sudoku
What is the maximum number of givens for a minimal Sudoku puzzle?...