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# Fourth International Meeting on Integer-Valued Polynomials, France

## December 7, 2020 - December 11, 2020

THE FOURTH INTERNATIONAL (HYBRID) MEETING ON INTEGER-VALUED POLYNOMIALS in Commutative and Non-Commutative Algebra and Related Problems will take place at the CIRM in Marseille, France, from 7 to 11 December 2020.

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

The subject goes back a century ago, with two papers of *G.** Pólya* and *A. Ostrowski* published in 1919 in the J*ournal de Crelle*. At the beginning, an integer-valued polynomial is a polynomial with coefficients in a number field, that takes integer values on the integers of the field and the study of the algebra of integer-valued polynomials takes place between commutative algebra and number theory. Since that time, interactions have been observed 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 and 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: algebra of polynomials with coefficients in matrices or quaternions.

The main goal of this fourth meeting is to allow researchers from different countries to meet and work together on those new areas. A particular atten-tion will be given to students and young reseachers who will be encouraged highly to present their research.