This meeting comes after three previous meetings about the same topic, also organized in the CIRM, in 1990, 2000, and 2010. Each of these meetings helped progress in research on ”Integer-valued Polynomials” in various areas.

– Combinatoric with the generalized factorials of Manjul Bhargava ;

– Discrete mathematics with, for example, the polynomial parametrization of sets of integers ;

– Number theory with the study of Polya fields and Polya groups, the use of the class field theory, the Lubin-Tate formal group laws, and Dirichlet series ;

– Commutative algebra : minimal generating sets, factorizations, spectrum, etc... ;

– p-adic analysis with the construction of polynomial normal bases of spaces of ultrametric functions ;

– Dynamical systems : discrete polynomial systems.

– Non-commutative algebra : algebras of polynomials with coefficients in matrices or quaternions.