**Speaker:** Daniele Bartoli

**Title: **Low-degree planar polynomials over finite fields of characteristic two

**Date/Time:** December 13,,2018 / 12:40 - 13:30

**Place:** FENS G015

**Abstract:** Planar functions are mappings from a finite field Fq to itself with an extremal differential property. Such functions give rise to finite projective planes and other combinatorial objects. There is a subtle difference between the definitions of these functions depending on the parity of q and we consider the case that q is even. We classify polynomials of degree at most q 1/4 that induce planar functions on Fq, by showing that such polynomials are precisely those in which the degree of every monomial is a power of two. As a corollary we obtain a complete classification of exceptional planar polynomials, namely polynomials over Fq that induce planar functions on infinitely many extensions of Fq. The proof strategy is to study the

**Contact:** Semih Onur Sezer