PostDoctoral Research Fellowship
Solutions of wave equations ("waves") model many different phenomena in physics, including sound, electromagnetism, and gravitation. During the tenure of the award, the PI published eight papers investigating the relationship between spacetime geometry and the long-time behavior of waves. The examples investigated include phenomena from several areas of physics, including cosmology (de Sitter space), diffraction (conic singularities), and particle physics (semilinear wave equations). One of the focuses of this study is an object called the "radiation field", which, given a wave, measures the radiation pattern seen by a distant observer. One surprising result during the tenure of the award relates the long-term behavior of this radiation field to a quantum object ("resonances") at infinity. Moreover, the reduced teaching load enabled the PI to take leadership roles in conferences and seminars related to the award. In particular, the PI organized three conferences at Northwestern University: a 2011 meeting for specialists in microlocal analysis, a 2012 meeting on evolution equations, and a 2014 meeting of the Midwest PDE seminar. The PI also mentored two undergraduate students, one graduate student, and served on two panels related to career development. Finally, the PI presented high level mathematics to undergraduates in several situations, including a lecture to the undergraduate math club and a lecture series at an undergraduate conference on mathematical quantum mechanics.
