Aaron Naber

Aaron Naber 2015 at the MFO

Aaron C. Naber (born November 16, 1982 ) is an American mathematician and mathematical physicist .

Aaron Naber studied mathematics at Pennsylvania State University with a bachelor's degree in 2005 and received his doctorate from Princeton University under Gang Tian in 2009 (Ricci solitons and collapsed spaces) . From 2009 to 2012 he was a Moore Instructor at the Massachusetts Institute of Technology , where he became an Assistant Professor in 2012 . In 2013 he became Associate Professor and in 2015 Kenneth F. Burgess Professor of Mathematics at Northwestern University .

It deals with geometric analysis and differential geometry with applications in physics ( Yang-Mills theories , Einstein manifolds ), in particular the development of Riemannian manifolds with Ricci flow and moderate curvature flow (mean curvature flow) and related Regularitätsfragen . A major problem in the proof of the Poincaré Conjecture by Grigori Perelman was the singularities of the Ricci River. In his dissertation he expanded the investigation from the three dimensions investigated by Perelman to four and more (with limited non-negative curvature) and investigated shrinking soliton solutions . Together with Gang Tian , he investigated the geometric structure of collapsing n-dimensional Riemannian manifolds with uniformly limited sectional curvature and, in particular, that a smooth orbifold structure results in four and fewer dimensions outside a finite number of points. In 2015 he and Robert Haslhofer succeeded in finding new estimates and a definition of weak solutions for the discontinuous case by embedding them in the investigation of the infinite-dimensional stochastic analytical structure of the Ricci River .

In 2014 he was a Sloan Fellow and invited speaker at the International Congress of Mathematicians in Seoul (The structure and meaning of Ricci curvature) . For 2018 he received the New Horizon in Mathematics Prize .

Fonts (selection)

• with Gang Tian: Geometric structure of collapsing Riemannian Manifolds, Part 1, Arxiv 2008 , Part 2, Arxiv 2009 (N * -bundles and Almost Ricci Flat Spaces)
• with Jeff Cheeger : Lower Bounds on Ricci Curvature and Quantitative Behavior of Singular Sets, Inventiones Math., Volume 191, 2013, pp. 321–339. Arxiv 2011
• Characterizations of Bounded Ricci Curvature on Smooth and NonSmooth Spaces, Arxiv 2013 .
• with Jeff Cheeger: Einstein Manifolds and the Codimension Four Conjecture, Annals of Mathematics, Volume 182, 2014, pp. 1093–1165, Arxiv
• with Tobias Colding : Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications, Annals of Mathematics, Volume 176, 2012, pp. 1173-1229. Arxiv 2011
• with Daniele Valtorta: Rectifiable-Reifenberg and the regularity of stationary and minimizing harmonic maps , Annals of Mathematics, Volume 185, 2017, pp. 131--227.
• with Robert Haslhofer: Ricci Curvature and Bochner Formulas for Martingales, Arxiv 2016
• with Wenshuai Jiang: L2 Curvature Bounds on Manifolds with Bounded Ricci Curvature, Arxiv 2016
• with Daniele Valtorta: Energy identity for stationary Yang-Mills, Arxiv 2016

Web links

• Homepage at Northwestern University

Individual evidence

1. ↑ Aaron Naber in the Mathematics Genealogy Project (English)
2. ↑ He published partial results even before his dissertation, Noncompact Shrinking 4-Solitons with Nonnegative Curvature , Arxiv 2007