Javier FresánUniversity Professor
Javier Fresán works in number theory and algebraic geometry. He is currently a professor at Sorbonne University, member of theInstitut de Mathématiques de Jussieu-Paris Rive Gauche1 , after holding a Monge professorship at École polytechnique (2017-2023) and post-doctoral stays at ETH Zürich (2014-2017) and MPIM Bonn (2013-2014). His research has won numerous awards, including the Dargelos Prize and the CNRS Bronze Medal in 2023, as well as a Frontiers of Science Award in the same year for his paper “A non-hypergeometric E-function”, in which he and his collaborator Peter Jossen answer a question formulated by Siegel almost a hundred years ago. He is editor-in-chief of the Documents Mathématiques collection and a member of the editorial board of Annales scientifiques de l'École normale supérieure and Commentarii Mathematici Helvetici. His exhibition skills have earned him invitations to Nachdiplom-Vorlesungen and several Bourbaki seminars. He is also the author of two books for the general public, translated from Spanish into a dozen languages.
- 1CNRS/Sorbonne Université/Université Paris Cité
EMOTIVE (Exponential Motives and Arithmetic Gevrey Series)
Exponential patterns are a powerful tool for studying a wide range of objects associated with a functionally algebraic variety, from exponential sums over finite fields in analytic number theory to Landau-Ginzburg models in mirror symmetry. The EMOTIVE project aims to apply the abstract theory of exponential patterns to concrete problems involving arithmetic Gevrey series. These are integer series that are solutions of a differential equation and satisfy certain growth conditions of an arithmetic nature. Depending on the precise form of these conditions, they fall into three main types: G-functions, E-functions and Э-functions. A host of fascinating questions surround these objects: what are the transcendence properties of their special values? What is the nature of their differential equations? Can they be represented by integrals from geometry? The most important examples of G-functions come from the period functions of brushes of algebraic varieties. The theory of exponential patterns suggests a geometric interpretation of E-functions that will be systematically exploited to make progress on these questions.
