All Questions

This question is about the content of this paper by J. Bourgain, N. Katz, T. Tao. In the final step (page 18) of the proof of Szemerédi-Trotter type theorem, we have already known $$|A''+A''|\lesssim ...

I was reading Adam Sheffer's book "Polynomial Methods and Incidence Theory" and I tried to solve the following exercise: Exercise 1.1 Construct a set $\mathcal{P}$ of $m$ points and a set $\...

Let $q$ be prime and let $q\delta \sim 1.$ Let $K$ be any set of $C_n\delta$-separated tubes in $B(0,2)$, where $C_n$ is some constant depending on $n$. Let us consider a grid of $q^n$ points scaled ...

Let A be a finite subset of $\mathbb{N}$, $\mathbb{R}$, or a sufficiently small subset of $\mathbb{F}_{p}$. Do we have a lower bound of the form $|A|^{1+\delta}$ on the following quantity: $$\max (|\...