Research Interests
My main interest is in harmonic/Fourier analysis. My PhD advisor was professor Shuanglin Shao. In one project, we considered extremizers for Strichartz inequality in dimension one. We provided an alternative proof of the fact that extremizers are Gaussians (originally proved by D. Foschi in his 2004 paper), but we also showed that extremizers are also real analytic. Since then, we have turned our attention to a fourth order differential equation, the fourth order Schrödinger equation, to see if we can find similar results.
For my master's thesis at ESU, I worked under the tutelage of Dr. Qiang Shi. Together, we used wavelet algorithms to pull information out of bird calls. The recordings for these were found at the Macaulay Library. For the original project, this required several programs, and was considered successful. I plan to streamline this process in the future, and use only python. If successful, I would also like to consider several birds from the family Mimidae to see if the process could distinguish the Mimids from the birds that are being mimicked.