All Articles

ISU Discrete Math Seminar

Author: Lona | Image: Lona

Speaker: Ting-Wei Chao (Carnegie Mellon University)

Title: Finite Field Kakeya Problem

A set K in the n-dimensional vector space FqnF_q^nFqn​ over finite field FqF_qFq​ is called a Kakeya set if it contains a line in every direction. Dvir proved that the size ∣K∣ is at least cnqnc_nq^ncn​qn, where cn=1/n!c_n=1/n!cn​=1/n! by using polynomial method. Recently, We improved the bound to cn=1/2n−1c_n=1/2^{n-1}cn​=1/2n−1, which is the best possible constant.