Motivic zeta functions and Bernstein polynomials.

The monodromy conjecture is one of the most important open problems in singularity theory. Igusa formulated the conjecture in the seventies, motivated by his study of p-adic zeta functions. It predicts a precise relation between arithmetic properties of an integer multivariate polynomial f and geometric properties of the solutions of the equation f=0 over the complex numbers. The goal of the project is to incorporate the expertise of the research group 'Algebraic geometry and number theory' in high level international collaboration in order to achieve a more profound understanding, and in the long run a solution, of the conjecture. The foreign research partners are established specialists in singularity theory, motivic integration and non-archimedean geometry, domains playing a key role in the study of the monodromy conjecture.

Keywords:De Rham cohomology, Splicing, Analytic milnor fibre, Zeta functions, Bernstein polynomials, Monodromy conjecture

Disciplines:Algebra, Geometry