In the fall of 2014 I will be teaching the third year course Essential PDEs. Here is the website for the course.
Slides from various expository talks I have given. For talks on current reseach see the research tab.
I am generally interested in inverse problems, PDES, and differential geometry. Inverse problems is the area of mathematics which studies the recovery of parameters in a differential equation from some observations of solutions to that equation. One of the main themes of my past and ongoing research has been the application of methods from micro local analysis to questions of stable invertibility for a variety of inverse problems in tomography and seismic imaging. A general heuristic for inverse problems is that stable inversion is possible if the singularities of the quantity to be reconstructed appear in the data, and I am interested in investigating applications of this general principleWhere links to pdf documents or arXiv are given below the linked versions are generally prior to peer review, and may not match the published articles.
Starting with my work on seismic imaging I have also become interested in models of wave propagation in complicated, possibly random, media. This can be combined with inverse problems by asking whether statistical properties of a random medium may be recovered based on observations of waves propagating through that medium.
What you don't think looking at my teaching, research, or CV is enough fun?!
Well then you may be interested to know that in my spare time I like to play viola in the band Vanity Pages.