Aaron Naber

Assistant Professor of Mathematics
Geometric Analysis

Aaron Naber, Assistant Professor of Mathematics as of 2012, joins the faculty following appointment as CLE Moore Instructor and NSF Fellow since 2009. He completed his PhD at Princeton University in 2009 under Gang Tian. Naber is a geometric analyst, whose program includes the study of manifolds with Ricci curvature bounds, in particular Einstein manifolds and Ricci solitons, but also extends to other areas of analysis. In an early collaboration with Tian, Naber did foundational work on the geometric analysis of collapsing Riemannian manifolds. One of his main results, to appear in Annals jointly with Toby Colding, introduces new ideas and techniques toward the singular behavior of limit spaces under lower Ricci curvature assumptions. This groundbreaking development in the study of Ricci curvature was followed with a series of proofs of conjectures relating to the structure of such spaces. In more recent work with Jeff Cheeger, Naber developed a methodology to improve results in regularity theory. The collection of ideas, centered around the notion of a Quantitative Stratification, have been used to prove the first Sobolev regularity estimates in a variety of nonlinear settings, including Einstein manifolds, minimal surfaces and harmonic maps between Riemannian manifolds.

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