My primary 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 models.
- D. Damanik, M. Embree, J. Fillman, and M. Mei,
Discontinuities of the Integrated Density of States for Laplacians Associated with Penrose and Ammann-Beenker Tilings, to appear in Exp. Math.
- S. Hong and M. Mei,
The Game of Life on the Robinson Triangle Penrose Tiling: Still Life, J. Cell. Autom. 17 (2023), no.3-4, 209–219.
- J. Fillman and M. Mei, Spectral properties of continuum Fibonacci Schrödinger operators,
Ann. Henri Poincaré 19 (2018), no. 1, 237-247.
- M. Mei and W. Yessen, Tridiagonal substitution Hamiltonians, Math. Model. Nat. Phenom. 9 (2014),
no. 5, 204-238.
- M. Mei, Spectra of discrete Schrödinger operators with primitive invertible substitution potentials,
J. Math. Phys. 55 (2014), no. 8, 082701, 22.
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.
- B. Baker Swart, S. Crook, L. Hall-Seelig, H. G. Grundman, M. Mei, and L. Zack,
Fixed Points of Augmented Generalized Happy Functions II: Oases and Mirages,
J. Integer Seq. 22 (2019), no. 5, Art. 19.5.5.
- B. Baker Swart, K. A. Beck, S. Crook, C. Eubanks-Turner, H. G. Grundman, M. Mei, and L. Zack,
Fixed points of augmented generalized happy functions, Rocky Mountain J. Math. 48 (2018), no. 1, 47-58.
- M. Mei and A. Read-McFarland, Numbers and the heights of their happiness, Involve 11 (2018), no. 2, 235-241.
- B. Baker Swart, K. A. Beck, S. Crook, C. Eubanks-Turner, H. G. Grundman, M. Mei, and L. Zack,
Augmented generalized happy functions, Rocky Mountain J. Math. 47 (2017), no. 2, 403-417.
Click here for the list of my mathematical articles on arXiv. Click here for the list of my mathematical articles on MathSciNet.
I've also done a bit of work on explanation as it relates to epistemology and cognitive science of mathematics
and I am currently working on a spatial sampling analysis on a synthetic mollusk.
I've supervised several undergraduate student projects in the above areas:
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