Yves André

Yves André
Name	Yves André
Birth date	1966
Birth place	Lyon, France
Nationality	French
Fields	Mathematics, Number theory, Algebraic geometry, p-adic Hodge theory
Alma mater	École Normale Supérieure, Université Paris Diderot
Doctoral advisor	Luc Illusie
Known for	p-adic Hodge theory, Hodge–Tate structures, p-adic differential equations

Yves André

Yves André is a French mathematician noted for work in number theory, algebraic geometry, and p-adic Hodge theory. He has held research and teaching positions at prominent institutions including the CNRS, University of Strasbourg, and the Institut des Hautes Études Scientifiques. His contributions connect themes from Grothendieck-era cohomology theories to modern approaches in p-adic analysis and arithmetic geometry.

Early life and education

Born in Lyon, France, André studied at the École Normale Supérieure (Paris) where he completed rigorous undergraduate and graduate training alongside contemporaries from French mathematical circles such as students of Jean-Pierre Serre-influenced programs. He earned a doctorate under the supervision of Luc Illusie at Université Paris Diderot (Paris 7), working within the intellectual milieu shaped by collaborators and predecessors including Alexander Grothendieck, Pierre Deligne, and Jean-Louis Verdier. His early formation included exposure to seminars at institutions like the Collège de France and interactions with researchers from the Institut des Hautes Études Scientifiques.

Mathematical career and positions

André's career has spanned research appointments at the Centre National de la Recherche Scientifique (CNRS), visiting positions at the Princeton University mathematics department and collaborations with members of the Institute for Advanced Study. He has been affiliated with the Centre de Recerca Matemàtica and held professorial or research roles at the University of Strasbourg and the École Polytechnique. André has participated in organizing programs at the Mathematical Sciences Research Institute (MSRI) and contributed to editorial boards of journals connected to Cambridge University Press and other scholarly publishers. He has supervised doctoral students who later joined faculties at institutions such as the Université Paris-Saclay and the Université de Bourgogne.

Research contributions

André's research addresses foundational problems at the intersection of algebraic geometry and number theory, notably in the development and application of p-adic Hodge theory and the theory of differential equations over non-archimedean fields. Building on ideas from Alexander Grothendieck and Pierre Deligne, he produced work on Hodge–Tate structures and period mappings, engaging with the frameworks of Hodge theory, de Rham cohomology, and étale cohomology. His investigations into the structural properties of p-adic representations and Galois representations contributed to understanding comparisons between cohomology theories, drawing on techniques from Fontaine's rings and theories developed by Jean-Marc Fontaine and Jean-Pierre Serre.

André introduced and advanced notions relating to the algebraicity and transcendence of periods, interacting with conjectures of André–Oort-type themes and with transcendence questions tied to special values studied by Gelfond and Schneider in earlier eras. He formulated results on the algebraic independence of values of solutions to functional equations, inspired by interactions with scholars such as Michel Waldschmidt and Gérald Tenenbaum. In p-adic differential equations, his work on indices, slopes, and the structure of differential modules over the Robba ring connects to research by Kiran Kedlaya and Christophe Dwork, advancing the understanding of irregular singularities in the non-archimedean setting.

André also contributed to the conceptual synthesis of motives, periods, and Galois symmetries, engaging with the legacy of Grothendieck's vision of motives and the later formalism advanced by Yves Hellegouarch and Alexandre Grothendieck's contemporaries. His expository and research writings clarified links between Tannakian categories and period conjectures, making bridges to work by Saavedra Rivano and Pierre Deligne.

Awards and honors

André has been recognized within the mathematical community through memberships and invitations to prominent venues. He received invitations to speak at leading assemblies such as the International Congress of Mathematicians satellite events and delivered lectures at the Collège de France and institutions including the Institut Henri Poincaré. He has been awarded grants and fellowships from national agencies like the Agence Nationale de la Recherche and held research distinctions within the CNRS system. André's papers have been cited and discussed in the context of prize-winning lines of inquiry by winners of awards such as the Sophie Germain Prize and the Grand Prix Paul Doistau–Émile Blutet in related areas.

Selected bibliography and publications

- "Period mappings and differential equations. From C to Cp" — monograph and lecture notes connecting Hodge theory, p-adic Hodge theory, and differential equations; influenced subsequent expositions by researchers at MSRI and IHÉS. - "Galois theory, motives, and transcendence" — survey articles relating motivic Galois groups to period conjectures and to approaches developed by Grothendieck and Deligne. - Papers on p-adic differential modules and the Robba ring, addressing irregularity and slope filtrations; these works engage with methods pioneered by Christophe Dwork, Kiran Kedlaya, and Jean-Marc Fontaine. - Expository contributions to volumes honoring Alexander Grothendieck and Pierre Deligne, synthesizing concepts from Tannakian categories and Hodge structures. - Research articles on algebraic independence and transcendence of periods, intersecting with literature by Michel Waldschmidt, Gelfond, and Schneider.

Category:French mathematicians Category:Algebraic geometers Category:Number theorists Category:Living people