On Thursday, 19.07.2018, at 16:15 in Arnimallee 3, SR 119
Daniele Bartoli (University of Perugia)
will give a talk on
Permutation polynomials over finite fields
Let q = p^h be a prime power. A polynomial f(x) in Fq[x] is a permutation polynomial (PP) if it is a bijection of the finite field Fq into itself. On the one hand, each permutation of Fq can be expressed as a polynomial over Fq. On the other hand, particular, simple structures or additional extraordinary properties are usually required by applications of PPs in other areas of mathematics and engineering, such as cryptography, coding theory, or combinatorial designs. Permutation polynomials meeting these criteria are usually difficult to find.
A standard approach to the problem of deciding whether a polynomial f(x) is a PP is the investigation of the plane algebraic curve Cf : (f(x) − f(y))/(x − y) = 0; in fact, f is a PP over Fq if and only if Cf has no Fq-rational point (a, b) with a != b.
In this talk, we will see applications of the above criterion to classes of permutation polynomials, complete permutation polynomials, exceptional polynomials, Carlitz rank problems, the Carlitz conjecture.
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