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# Manifolds of bounded Ricci curvature and the codimension $4$ conjecture

## Kähler Geometry, Einstein Metrics, and Generalizations March 21, 2016 - March 25, 2016

March 22, 2016 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Jeff Cheeger (New York University, Courant Institute)
Location: MSRI: Simons Auditorium
Tags/Keywords
• algebraic geometry and GAGA

• mathematical physics

• complex differential geometry

• Kahler metric

• mirror symmetry

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

#### 14462

Abstract

Let $X$ denote the Gromov-Hausdorff limit of a noncollapsing sequence of riemannian manifolds $(M^n_i,g_i)$, with uniformly bounded Ricci curvature.  Early workers conjectured (circa 1990) that $X$ is a smooth manifold off a closed subset of Hausdorff codimension $4$.  We will explain a proof of this conjecture. This is joint work with Aaron Naber.

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