IMI Colloquium

高度情報処理は、最近数学外の分野でよく耳にする言葉だが、発表者は、回折データから材料のミクロ情報を読み解く数学的手法開発に長年携わってきた。特に、 「格子決定」「位相回復」という二つのテーマ、その代数学・整数論との意外な関係が、この応用研究を現在まで続けてきた理由である。

代数学や調和解析の典型的な問題と異なり、計測技術を駆使して取得されたデータの真の姿はノイズや様々な因子、有限性の向こう側にある。この自然の声を通 して得られた数学を紹介する。

Title : Advanced informatics recently applied to data analysis in materials science

Abstract :
Recently, I often hear ``Advanced informatics'' outside mathematics, which is what this title means. For long, I have been working for development of mathematical techniques to extract angstrom-size information from diffraction data. In particular, ``lattice determination'' and ``phase retrieval'' of material samples have various mysterious links to algebra & number theory, which are the reason I'm ceaselessly working in this application field.

Differently from the typical problems in algebra or harmonic analysis, the ``real data'' obtained by the highest-technology facilities are under influence of noise, various factors and some kind of finiteness. This nature voice is always leading me to new findings of mathematics, which I'd like to present in my talk.