Number of points with integer coordinates in a closed domain, number of solutions of diagonal diophantine systems (Olivier Robert, MCF at the Institut Camille Jordan, Combinatorics and Number Theory team) Partnerships with colleagues from ENS Lyon, University of Göttingen (Germany) and University of Gottenbörg (Sweden)
Number Theory is a branch of mathematical research concerned with questions of arithmetic, such as the study of particular families of integers. One of the most famous categories of integers is that of primes. Although primes are very old (ancient), they still hold a lot of mystery, and remain at the heart of many current questions. Questions of arithmetic, through the centuries, have given rise to different currents and techniques, which belong to different mathematical fields
Amongst these is a field called Analytical Number Theory: this involves using analytical tools (functions, sequences, integrals, ….) to elucidate the structure of certain sets constructed using integers. These techniques are varied and allow a statistical (or macroscopic) view of certain sets of integers that have a priori erratic behaviour.
At the Institut Camille Jordan, Olivier Robert’s research work focuses on questions of Analytical Number Theory. Among these are two categories.