Takashi Satomi

I am Takashi Satomi, and am studying mathematics.
My main interests are harmonic analysis and functional analysis.
In particular, I am studying the refinement of Young's inequality on locally compact groups and Lie groups.
This inequality is a fundamental tool of functional analysis, and the (optimal) constant for which this inequality is optimal is explicitly determined by Beckner (1975) on locally compact abelian groups.
On the other hand, this optimal constant has not been determined as of April 2024 even for the most basic simple Lie groups, including special linear groups.
Determining this optimal constant explicitly is one of my research goals.

This inequality is related to various theories such as:

Hausdorff-Young inequality (harmonic analysis)
Brascamp-Lieb inequality (real analysis)
Brunn-Minkowski inequality (geometry)
Ruzsa's inequality (combinatorics)
uncertainty principle (quantum mechanics)
expander graph (graph theory).

I am also interested in the relationship between these and various other fields.

Research History

2019.4-2023.3 Graduate School of Mathematical Sciences, The University of Tokyo, PhD student
2023.4-2024.3 Graduate School of Mathematical Sciences, The University of Tokyo, associate fellow
2024.4- iTHEMS, Special Postdoctoral Researcher