Polynomials over Finite Fields: Functional and Algebraic Properties
Month: May 2014
Date: May 19--23
Name: Polynomials over Finite Fields: Functional and Algebraic Properties
Location: Centre de Recerca Matematica, Bellaterra, Barcelona, Spain.
The theory of polynomials over finite fields is fundamental for the study of finite fields, which in turn plays a central role in many areas of pure and applied mathematics. This is a classical area of mathematics with a rich history, going back to Gauss and Galois. The exciting and challenging problems concerning univariate and multivariate polynomials over finite fields are of intricate algebraic and number theoretic flavour and their study requires deep mathematical and computational tools. The determination and construction of special types of (irreducible, primitive, permutation) univariate and multivariate polynomials, for example, as well as understanding many of their functional and algebraic properties (composition, decomposition, iteration, factorization, size of value sets) are long standing problems in the theory of finite fields. These areas have attracted further attention in recent years due to their applications in cryptography, coding theory, combinatorics, design theory, quasi-Monte Carlo methods, communications.