associate professor
tukamoto (please add
Research Area
Differential Geometry, function 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 holomorphic maps from the complex plane ([1,3]).
(2) Dynamical systems in 4-dimensional gauge theory ([2]).
(3) Problem of embedding a dynamical system into the shift on the Hilbert cube ([4]).

Main papers:

[1] M. Tsukamoto, Deformation of Brody curves and mean dimension, Ergod. Th. & Dynam. Sys. 29 (2009) 1641-1657.
[2] S. Matsuo, M. Tsukamoto, Instanton approximation, periodic ASD connections, and mean dimension, J. Funct. Anal. 260 (2011) 1369-1427.
[3] S. Matsuo, M. Tsukamoto, Brody curves and mean dimension, to appear in J. Amer. Math. Soc.
[4] E. Lindenstrauss, M. Tsukamoto, Mean dimension and an embedding problem: an example, to appear in Israel J. Math.