Prof. Dr. Erwan Rousseau

CV

I am Professor of Mathematics at Aix-Marseille University since 2011 and Junior IUF fellow since 2016. Previously I was Maître de Conférences in Strasbourg University (2006-2011). My PhD thesis dates back to 2004 under the direction of Gerd Derthloff at Brest University. My former PhD students are B. Cadorel (2018) and J. Restrepo Velasquez (2018).

My main mathematical interests are in complex analytic and algebraic geometry, in particular questions related to the distribution of entire curves (and conjecturally on the arithmetic side, rational points) in algebraic varieties.

Selected Publications

• E. Rousseau : Equations diff ´ erentielles sur les hypersurfaces de P4, J. Math. Pures Appl. (9) 86 (2006), no. 4, 322–341.
•  G. Pacienza, E. Rousseau : On the logarithmic Kobayashi conjecture, J. Reine Angew. Math. 611 (2007), 221–235.
• S. Diverio, J. Merker, E. Rousseau : Effective algebraic degeneracy, Invent. Math. 180 (2010), no. 1, 161-223.
• X. Roulleau, E. Rousseau : Canonical surfaces with big cotangent bundle, Duke Math. J. 163 (2014), no.7, 1337–1351.
• E. Rousseau : Hyperbolicity, automorphic forms and Siegel modular varieties, Ann. Sci Ec. Norm. Super. (4) 49 (2016), no. 1, 249–255.

FRIAS Research Project

On hyperbolicity in complex geometry

This project is concerned with pure mathematics, more specifically complex geometry and its conjectural interactions with arithmetic on the existence of solutions of polynomial equations. The importance of these questions is illustrated by Faltings’s proof of the Mordell conjecture on the finiteness of rational points on algebraic curves of genus greater than 1. The project is based on questions in complex geometry whose solution resides in positivity properties of certain geometric structures. This positivity is most often expressed in geometric consequences (on entire curves) and arithmetic (on rational points).

Three directions can be seen to structure this project:

1. Holomorphic foliations: we study how the positivity of the canonical bundle impacts the existence on projective varieties of entire curves tangent to foliations.
2. Orbifold structures: the success of the minimal model program and recent works of Campana and Miyaoka show that the use in hyperbolicity of the logarithmic pairs of birational geometry is promising.
3. Singular varieties: we plan to investigate hyperbolic properties of singular varieties such as singular quotients of bounded symmetric domains.