IHES Annual Report 2020 | 25

Emmanuel ULLMO Mathematics, director of IHES since 2013.

Since July 2020, JEAN PIERRE BOURGUIGNON has taken over the interim presidency of the European Research Council (ERC).

EMMANUEL ULLMO, in collaboration with Gregorio Baldi, obtained two results on non-arithmetic ball quotients. The hyperbolic Ax-Schanuel theorem in this framework which is an optimal statement of functional transcendence and the finitude of maximum totally geodesic submanifolds. The method used for this combines ideas from Hodge theory (morphisms and domains of periods, Simpson's point of view), rigidity, functional transcendence and o-minimality. In collaboration with Rodolphe Richard, Emmanuel Ullmo continued his study of the equidistribution of totally geodesic subvarieties of Shimura varieties. By mixing homogeneous dynamics in the style of Ratner-Margulis

with o-minimal ideas, he obtained a general statement in

SCIENTIFIC ACTIVITY

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r Jean Pierre BOURGUIGNON Mathematics, professor emeritus and former director of IHES from 1994 to 2013, Nicolaas Kuiper Chair since 2013.

DISTINCTIONS

Prix Élie Cartan, Académie des sciences de Paris (2006) Invited Speaker ICM (2002) Institut Universitaire de France, junior member (2003-2008) Academia Europaea, membre (2015)

PUBLICATIONS

With C. Daw, A. Gorodnik and J. Li The Space of Homogeneous Probability Measures on the Maximal Satake Compactification of a Shimura Variety is Compact Pre-publication arXiv:1910.04568.

With G. Baldi Special Subvarieties of Non Arithmetic Ball Quotients and Hodge Theory Pre-publication arXiv:2005.03524.

DISTINCTIONS

CNRS Bronze Medal (1977) Prix Paul Langevin, Académie des sciences de Paris (1987) Prix des Sciences Physiques et Mathématiques, Comité du Rayonnement Français (1997) Doctor Honoris Causa, Keio University, Japan (2008) Doctor Honoris Causa, Nankai University, China (PR.) (2011) Doctor Honoris Causa, University of Edinburgh, United Kingdom Academia Europaea, member

Spanish Royal Academy of Sciences, foreign member Portuguese Academy of Sciences, foreign member London Mathematical Society, honorary member (2006) Deutsche Mathematiker Vereinigung, honorary member Polish Mathematical Society, honorary member

Editor of: Birkhäuser Monographs in Mathematics Journal of Mathematics and Music

The Director's Chair is supported by