Analysis, Dynamics and Applications Seminar

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.