고두원

Main purpose of this talk is to introduce a connection between restriction estimates for cones and point-sphere incidence theorems in the finite field setting. First, we review the finite field restriction problem for cones and address new results on the conical restriction problems. In particular, we establish the restriction conjecture for the cone in four …

Let ${\mathbb{F}}_q$ be a finite field of order $q$ which is a prime power. In the finite field setting, we say that a function $\varphi :{\mathbb{F}}_q^d\times {\mathbb{F}}_q^d\to {\mathbb{F}}_q$ is a Mattila-Sjölin type function in ${\mathbb{F}}_q^d$ if for any $E\subset {\mathbb{F}}_q^d$ with $|E|\gg q^{\frac{d}{2}}$, we have $\varphi (E,E)={\mathbb{F}}_q$. The main purpose of this talk is to present …