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Monotonicity, Small Eigenvalues, and Nonlinear PDE

Analysis, Dynamics, and Applications Seminar

Monotonicity, Small Eigenvalues, and Nonlinear PDE
Series: Analysis, Dynamics, and Applications Seminar
Location: MATH 402
Presenter: Mark Stern, Department of Mathematics, Duke University

Monotonicity techniques developed to study the small-scale structure of singularities of nonlinear pdes have been sharpened to give large scale information about eigenfunctions with small eigenvalues. These improved monotonicity estimates can then return to nonlinear pde to provide better understanding of their singularities. In this talk, I will discuss various applications of monotonicity estimates to eigenvalue problems arising in topology and number theory and will conclude with an application to a toy problem concerning singularities arising in Yang Mills theory.