Research Interests

I am interested in problems in partial differential equations, spectral theory, microlocal analysis, global analysis, and nonlinear waves.

 

I have used spectral and microlocal techniques to study the relationship between pointwise wave decay and the underlying geometry, and Klainerman vector field methods to study the existence of solutions to systems of quasilinear wave equations.

 

Currently, I am investigating the effect of trapping on a dispersive estimate called local energy decay. The local energy decay estimate is a central tool for studying nonlinear waves and for analyzing wave behavior on asymptotically flat manifolds.

 

See my research statement for a more detailed discussion of my work.

Publications

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  1. K. Morgan. The effect of metric behavior at spatial infinity on pointwise wave decay in the asymptotically flat stationary setting. 48 pages. (View Pre-print)
     

  2. J. Metcalfe & K. Morgan. Global existence for systems of quasilinear wave equations in (1+4)-dimensions. Journal of Differential Equations. 2020. (https://doi.org/10.1016/j.hde2019.09.012)
     

  3. K. Morgan. Wave decay in the asymptotically flat stationary setting. 2019, 155 pages. Available from ProQuest Dissertations and Theses Global. (2296357806)

Selected Talks

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* indicates talk aimed at undergraduates

Invited Talks

  • AMSI-ANU Workshop on Microlocal Analysis (March 2018)
    South Durras, Australia 
    View Talk Slides
     

  • Department of Mathematics Research Week Event* (October 2017)
    UNC Chapel Hill 
    View Talk Slides

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Other Talks

Notes