Liouville quantum gravity and SLE

• Jason Miller (Cambridge University)

Room: Amphi Laurent Schwartz There has been tremendous progress in the mathematical study of two dimensional statistical mechanics models at criticality in the last 25 years. This was initially catalyzed by the discovery of the Schramm-Loewner evolution (SLE; the canonical model for a conformally invariant random planar curve) and later by the mathematical formulation of Liouville quantum gravity (LQG; the canonical model for a random two-dimensional Riemannian manifold). We will discuss the history and recent developments in the study of SLE and LQG, the deep connections between them as well as their discrete and combinatorial counterparts.

Geometry and Analysis with Ricci Curvature

• Aaron Naber (Northwestern University)

Room: Amphi Laurent Schwartz In this talk we introduce and survey results about the structure of manifolds with lower and bounded Ricci curvature. We begin with some elementary background, and work our way through the results of the decades, mostly attempting to explain in the form of examples. We will end with an explanation of the state of the art, including the known regularity of Einstein manifolds and the structure of their singularities, maybe stating some open questions and conjectures along the way.

Remise des prix

• Franck Barthe (Institut de Mathématiques de Toulouse)
• Odile Rauzy (Université Paul Sabatier)

Room: Amphi Laurent Schwartz