Research Interests: My research interests are in analysis and mathematical physics with a focus on investigating spectral properties of quantum lattice models. Tools for analyzing quantum lattice models come from a wide range of mathematics. While I predominantly use techniques from analysis, I also use elements of representation theory, complex analysis, and perturbation theory.

My current research focuses on determining the existence and stability of non-vanishing spectral gaps above the ground state energy, with an emphasis on multi-dimensional systems. Applications of my work are found in condensed matter physics, quantum information theory, and quantum computation.
 
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