Number of points with integer coordinates in a closed domain, number of solutions of diagonal diophantine systems (Olivier Robert, MCF at Institut Camille Jordan, Combinatoire et Théorie des Nombres team) Partnerships with colleagues at 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 prime numbers. Although prime numbers are very old (antiquity), they still conceal a great deal of mystery, and remain at the heart of many current questions. Over the centuries, arithmetic questions have given rise to a variety of currents and techniques in different mathematical fields.
Among these is a field called Analytical Number Theory: the aim is to use the tools of analysis (functions, sequences, integrals, ….) to elucidate the structure of certain sets constructed using integers. These techniques are varied and provide a statistical (or macroscopic) view of certain sets of integers that a priori exhibit erratic behavior.
At the Institut Camille Jordan, Olivier Robert’s research focuses on questions of Analytical Number Theory. Among these are two categories.
