associate professor
tukamoto (please add
Research Area
ergodic theory, dynamical systems

My main research area is the theory of mean dimension. Mean dimension is a topological invariant of dynamical systems introduced by Gromov in 1999.
While his motivation is to propose a new approach to infinite dimensional dynamical systems in geometric analysis, Elon Lindenstrauss and Benjamin Weiss found several applications of mean dimension to topological dynamics. I have studied both geometric analysis approach and topological dynamics approach to mean dimension theory. More concretely I have been studying the following three themes.

(1) Dynamical systems of entire holomorphic curves ([1,2]).
(2) Compressing and embedding topological dynamical systems ([3]).
(3) Variational principle between rate distortion theory and mean dimension theory ([4]).

Main papers:

[1] S. Matsuo, M. Tsukamoto, Brody curves and mean dimension, J. Amer. Math. Soc. vol.28 (2015) 159-182.
[2] M.Tsukamoto, Mean dimension of the dynamical system of Brody curves, Invent. math. vol.211 (2018) 935-968.
[3] Y. Gutman, E. Lindenstrauss, M. Tsukamoto, Mean dimension of $\mathbb{Z}^k$-actions, GAFA, vol.26 (2016) 778-817.
[4] E. Lindenstrauss, M. Tsukamoto, From rate distortion theory to metric mean dimension: variational principle, to appear in IEEE Transactions on Information Theory.