One of my research interests involves the application of dynamical systems (uniformly hyperbolic, partially hyperbolic, symbolic) to mathematical physics. Specifically, I use dynamical techniques to investigate spectral properties of operators involved in the study of quasicrystals. I'm also interested in conducting numerical experiments related to the long-term behavior of several specific dynamical systems.
Another one of my research interests lies in number theory and integer sequences. Think of a number, now square the digits and sum that. What do you get? If you keep iterating this procedure, you will either end up at a 1 or a 4. If you end up at a 1, the number you started with is called a happy number. I study several generalizations of this procedure.
- M. Mei and W. Yessen, Tridiagonal substitution Hamiltonians,
Math. Model. Nat. Phenom. 9 (2014), no. 5, 204-238. [arXiv:1312.2259]
- M. Mei, Spectra of discrete Schrödinger operators with primitive invertible substitution potentials,
J. Math. Phys. 55 (2014), no. 8, 082701, 22pp. [arXiv:1311.0954]
- B. Baker Swart, K. Beck, S. Crook, C. Eubanks-Turner, H. Grundman, M. Mei, and L. Zack, Fixed Points of Augmented Happy Functions, in preparation.
- M. Mei and A. Read-McFarland, Numbers and the Heights of their Happiness, submitted.
- B. Baker Swart, K. Beck, S. Crook, C. Eubanks-Turner, H. Grundman, M. Mei, and L. Zack, Augmented Generalized Happy Functions, to appear in the Rocky Mountain Journal of Mathematics.