It is a major insight of the preceding two centuries that one can use a geometrical language to study the solutions of a given set of polynomial equations with coefficients in an arbitrary field, such as the complex numbers or even in an arbitrary ring, such as the integers. The corresponding objects, called algebraic varieties, are extremely rich and mysterious due to their dual nature, geometric and arithmetic.

The driving force of the project is the use of the recent and powerful theory of motivic A1-homotopy introduced by Voevodsky to produce new, and study classical, invariants of algebraic varieties of both geometric and arithmetic nature.

The expected applications have a very wide range: advances in the understanding of Voevodsky’s theory, producing new knowledge in affine algebraic geometry, extending previously known computations of invariants for families of algebraic varieties, and improvement of our arithmetical knowledge of certain kinds of algebraic varieties.

- As part of the present project, the Institute of Mathematics of Burgundy in Dijon is recruiting a post-doctoral fellow. The recruited person will carry out his research within the team "Géométrie et Système Dynamiques" on the themes of Algebraic Geometry in the broad sense, with a more specialized component on affine varieties, moduli spaces, motivic homotopy theory and derived categories. More information available HERE .
- As part of the present project, the Laboratory of Mathematics of Besançon is recruiting a post-doctoral researcher in the fields of arithmetic geometry, algebraic number theory and analytic number theory. The successful applicant will join the group “Algebra and Number Theory” of the LmB a nd will interact with its different members. More information available HERE .

- Journée I-SITE Besançon-Dijon, January 31 2019, LMB, Besançon.