Perception of mathematicians
Stories about mathematicians and their eccentricity or outlandish behavior are fun and popular with the public. As a result, an image of mathematicians (one suitable for writing or film) as being solitary and a hair’s breadth away from madness has been created and this is something I do not appreciate. I picture an average mathematician to be naïve, slightly obsessed, almost too honest, and unable to lie.
My research is in the interdisciplinary field of number theory and ergodic theory.
Number Theory and Ergodic Theory
Both are broad fields with very long histories. In several mathematical problems, there is a difference between analog and digital, and between discrete and continuous. In the case of many discrete problems, describing the problem is easy, but solving it can be difficult. It is easy to provide many examples of notoriously hard problems in discrete mathematics. Few of these can be solved, and often there are no helpful hints or clues. Therefore, number theory researchers find it interesting when even a slight headway is made in such problems. Ergodic theory was born with the development of statistical mechanics. It is a study of the average and broad characteristics of particle trajectories in a closed system. What is important in this theory is a sort of “pre-established harmony.” One may guess the final goal intuitively; however, often times, he/she is unable to make it rigorous. That, is the character of this field.
Example of quasi-self-similar tiling
Strongly non-periodic tiling by Ammann
I am currently interested in tiling dynamical systems. The classification problem of tilings existed for a long time. However, studying its dynamical system is a relatively recent trend. These dynamical systems, appearing naturally in relation to number-theoretic algorithms, become relatively non-chaotic and solid dynamical systems. They can be studied using various tools such as algebra, geometry, analysis, and information mathematics, and many other fields of mathematics can be applied. In 2011, Shechtman received the Nobel Prize in Chemistry for the discovery of quasicrystals. One of the goals in tiling dynamical systems research is to create a model for the structure of these quasicrystals.
Image of conversion of quasi self-similar tiles above to self-similar tiles
Am I suited for mathematics?