updated on 8 May 2025


Hiroyuki Chihara



College of Education
University of the Ryukyus
Nishihara, Okinawa 903-0213, Japan
9 December 2024
University of Auckland
New Zealand

I am a mathematician. I have a strong interest in visualizing internal states that cannot be directly observed using only external data. In 2020, I ventured into a new research area that I refer to as the "microlocal analysis in integral geometry." In this field, I work with linear operators such as the geodesic X-ray transform, which maps a function on a Riemannian manifold to its integrals along geodesics. My approach begins with an examination of its fundamental properties as a Fourier integral operator, through which I gain new insights.

A straightforward example of this is the X-ray transform on the plane, which is the theoretical data produced by a CT scanner capturing cross-sections of the human body. Microlocal analysis focuses on the singularities of Schwartz distributions, such as contours in an image, by decomposing them directionally at each singular point. Although the Euclidean space setting is often too concrete and simple to see the underlying principles, in the more abstract framework of Riemannian manifolds it sometimes becomes clearly visible.

Unfortunately, this area of research remains relatively unknown in Japan. However, it is a thriving field internationally, with many prominent mathematicians contributing to its development. So I actively participate in research conferences and webinars abroad.


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