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You are here: FRIAS Fellows Fellows 2019/20 Prof. Dr. Philippe Eyssidieux

Prof. Dr. Philippe Eyssidieux

Université Grenoble Alpes
External Senior Fellow
Marie S. Curie FCFP Fellow
March - May & July 2018


I am Professor of Mathematics at the Université Grenoble-Alpes since 2005 and was  Junior IUF fellow in 2010-2015. Previously a Chargé de Recherches CNRS  at the Université Toulouse III,  my PHD thesis dates back to 1994 under the direction of Ngaiming Mok at the Université Paris-Sud. My four former PHD students are J. Keller (2005),  D. Mégy (2011), M. Spinaci (2013), T. Delcroix (2015).

My main mathematical interests are in Complex Differential and Algebraic Geometry, applications of Complex and Geometric Analysis therein and fundamental groups of algebraic varieties.

Selected Publications

  • Eyssidieux, P. Guedj, V. et Zeriahi, A. Singular Kähler-Einstein metrics, Journ. Amer. Math. Soc. 22 (2009), 607-639.
  • Eyssidieux P., Katzarkov L., Pantev T., Ramachandran M.: Linear Shafarevich conjecture. Annals of Math. 176 (2012), 1545--1581.
  • Campana, F., Claudon, B., Eyssidieux P.: Représentations linéaires des groupes kählériens: Factorisations et conjecture de Shafarevich linéaire, Compositio Mathematica, 151 (2015)  351-376.
  • Eyssidieux, P., Mégy, D.: Sur l'application des périodes d'une Variation de Structures de Hodge attachée aux familles d' hypersurfaces à singularités simples, Commentarii Mathematici Helvetici 90 (2015), 731-759.
  • Eyssidieux, P.: Orbifold Kähler groups and the Shafarevich conjecture for Hirzebruch's covering surfaces with equal weights. arXiv:1611.09178, to appear in Asian J. Math.

FRIAS Research Project

New Kähler groups

The Serre problem aims at identifying the fundamental groups of smooth complex algebraic varieties among finitely presented groups and admits several variants (the projective case, the Kähler case and their orbifold versions). Considerable progress on the Kähler case has been achieved in the last 30 years, but further progress will require new examples. The constraints governing the Serre problem or more generally the homotopy type of smooth complex algebraic varieties originate typically in Hodge theory: many natural homotopical invariants carry mixed Hodge structures. However this is not enough. Indeed the part of a Kähler groups that is killed by all finite dimensional representations seems to be invisible when wearing just Hodge theoretical glasses.