Aaron Naber, Professor of Mathematics from the Institute of Advanced Study, Princeton, is set to give a distinguished lecture and a seminar the week of October 20-24, 2025.
The lecture will be on October 22, 2025, at 4pm in B239 Van Vleck Hall.
The title is Structure of Singular Sets: Nonlinear Harmonic Maps and the Energy Identity.
Abstract: We begin this talk with an introduction to linear and nonlinear harmonic maps between Riemannian manifolds, with a first goal of understanding some basic examples and uses in geometry and analysis. Unlike linear harmonic maps, which are always smooth and well behaved, nonlinear harmonic maps may exhibit singularities of various sorts. One type of singularity which appears is in the form of discontinuous points of a fixed solution. Another which appears is in the form of blow up not for a single solution, but for a sequences of solutions. We will give examples and discuss how they relate to the general theory, attempting to end at an explanation of the regularity theory and energy identity of nonlinear harmonic maps. Work discussed is joint with Daniele Valtorta.
The seminar will be on October 23, 2025 at 4pm in 22 Ingraham Hall.
The title is Structure of Singular Sets: Recent Progress on Manifolds with Ricci Curvature Bounds.
Abstract: In this talk we survey some of the recent advances made in the understanding of manifolds with lower and two sided Ricci curvature bounds. We will discuss the structure theory of such spaces, both in terms of singularities and in terms of topological behavior, with an emphasis on using examples to explain recent advances. We will discuss some open problems and directions.