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Research
My mathematical world lies at the interface of topology, analysis and dynamical systems. I use topological methods to understand the spectra of linear differential operators. The main tool in my arsenal is the Maslov index, an intersection index for a path of Lagrangian planes. During my PhD, I have developed index theorems for one-dimensional Hamiltonian differential operators on both bounded and unbounded domains, with applications to the stability analysis of nonlinear waves.
Check out my slides from my award-winning talk.
Papers and preprints
- Hamiltonian spectral flows, the Maslov index, and the stability of standing waves in the nonlinear Schrodinger equation. SIAM Journal on Mathematical Analysis (SIMA). 55 (5) pp. 4998-5050. DOI:10.1137/22M1533797. With Graham Cox, Robert Marangell and Yuri Latushkin (2023). (pdf)
- Detecting eigenvalues in a fourth-order NLS equation with a non-regular Maslov box. In preparation.
PhD Thesis
- Hamiltonian spectral theory and the Maslov index. (pdf)