2024 December

Speaker:

富安 亮子 氏（九州大学）

Ryoko Oishi-Tomiyasu (Kyushu University)

学部より数学・数理科学専攻。修士から織田孝幸先生の研究室（保型形式を中心とする数論）。博士課程最後の年に国立大学が法人化。2004年企業のソフトウェアエンジニア（研究職）に就職。2005年、数論の考え方が有用な粉末結晶構造解析を中心とする数理結晶学に出会う。手法・ソフトウェア開発に関わる予想以上の成果が勤務中に続けて得られ、2007年アカデミアに戻ることを決意。数学ではなく、高エネ研（KEK, 物理）のポスドクの特任研究員・特任助教として、粉末結晶構造解析に関わる手法・ソフトウェア開発のプロジェクトを継続する。若い頃の研究として未知の結晶格子解析のためのCONOGRAPH (Conway’s topograph)の手法・ソフトウェア開発・公開を行い、代数・数論の新しい応用を実現する。2014年に第2期さきがけの数学領域に応募し採択。大学に戻って研究継続を決意し、東北大学AIMR、山形大学理学部を経て、2019年より九州大学IMI准教授、2022年より教授 。

I majored in mathematics at the University of Tokyo, in particular, number theory and automorphic forms in the laboratory led by Prof. Oda Takayuki in the master's and doctoral courses. In the final year, Japanese national universities were transformed into national university cooperations. I took a research software engineering job in a company in 2004. I encountered with mathematical crystallography (including powder crystal structure analysis) in 2005 and found that ideas from number theory were useful in this field. In 2007, due to successive results beyond expectations in algorithm and software development, I decided to return to academia, not in mathematics, but as a projective researcher/projective assistant professor at KEK (High Energy Accelerator Research Organization, Physics), and to continue the software-related project I had been involved in for three years. As a young researcher before getting a tenure, I developed methods for the software CONOGRAPH (Conway’s topograph) for ab-initio crystal lattice analysis, and realized new applications of algebra and number theory. At the time, the “postdoc problem” was becoming widely known. My proposal for the second term of PRESTO in mathematics was accepted in 2014. I decided to move a university and continue my research. After working at the AIMR of Tohoku University and the Faculty of Science of Yamagata University, as an associate professor (2019--) and a professor (2022--). 

Title (first part):

数の幾何・微分幾何による数理植物学の黄金角の方法の一般化について

Generalized golden angle method derived from ideas of mathematical botany, geometry of numbers and differential geometry

Abstract (first part):

上述の未知の結晶格子の解析や位相回復の他、パッキングやタイリングも数理結晶学の典型的な問題である。最近開発した、ユークリッド空間を含む、対角化可能な計量を持つリーマン多様体上の多様な点パッキングを生成できる、黄金角の方法の一般化について紹介する。この一般化には、数の幾何のマルコフ理論と、斉次線形式の積に関するDavenportの定理が用いられ、この方法が任意のC^\infty曲面に適用できることの証明には、準線形双曲型偏微分方程式の一般論が用いられた。得られた手法をさらに拡張するには、数論におけるいくつかの未解決問題を解決する必要があり、こういった問題に取り組むことも私の専門分野の一つの側面だが、他方、科学でよく知られた現象のより正確な理解をもたらしたこの研究は、境界領域の数学研究らしい側面もある。この研究の大枠を事前に理解するには、以下のウェブ記事を参照可能: https://www.kyushu-u.ac.jp/f/59085/24_10_04.pdf

In addition to the above-mentioned ab-initio crystal lattice analysis and phase recovery, packing and tiling are also typical problems in mathematical crystallography. I will talk about the generalized golden angle method we recently developed to generate various types of point packing on Riemannian manifolds with diagonalizable metrics including the Euclidean spaces. This generalization makes use of Markov theory and Davenport's theorem on the product of homogeneous linear forms in geometry of numbers. To show that the method can be applied to any C^\infty surfaces, the general theory of quasilinear hyperbolic partial differential equations was used. To further extend the new method, it is necessary to solve some open problems in number theory. Working on such problems is one aspect of my areas of expertise, but this research, which has brought about a more precise understanding of the well-known phenomenon in science, seems to illustrate what mathematicians can expect from interdisciplinary research. For an overview of this research, you can see the following web article: https://www.kyushu-u.ac.jp/f/59085/24_10_04.pdf

Title (second part):

数学コミュニティの境界や外部で数学をする方法

Methods for working as a mathematician at the boundary or outside the mathematical community

Abstract (second part):

学際的研究は、数学を発展させ得る方法の一つです。物理の研究者からは、若い研究者の処世術について率直なアドバイスを受けましたが、彼らは数学分野をどう思うかもよく話したので、ある時点で、彼らが物理やその隣接分野を言語化する教育がされており、逆方向（数学から科学へ）の関心が少ないことに気づきました。別の影響は、彼らのコミュニティ・カルチャーから示唆される、数学のコミュニティ・カルチャーの潜在的な可能性についてです。例えば、(1)数学にノーベル賞があったら？ (2) 複数分野が意見交換できる大きな国際会議が主要なイベントであったら？ (3)それぞれの数学研究者が日常言語で一般向けに研究の有用性や意義を説明する必要があったら？ (4)日常的に手短に他分野の情報を耳にする機会があったら？数学の多様性はどのような影響を受けるでしょうか？　とんでもない質問かもしれませんが、制度設計は全てに影響します。多様性や学問の自由を守るため個人でできることを挙げてみたいと思います。

Interdisciplinary research is one of the ways to develop the mathematical community. I used to get a lot of frank advice for young researchers from physicists. They also told me a lot about their impressions and thoughts on mathematicians. At a certain point, I realized that they were educated to be able to do so for their own fields and adjacent fields, and there seemed to be less interest in the opposite direction (from mathematics to science). The way of scientific community and culture also gives many good ideas of what makes the mathematical community and culture the way it is. To see this, we can ask: (1) What if there were a Nobel Prize in mathematics? (2) What if large international conferences were the main events for mathematicians? (3) What if mathematicians from all the fields had to explain their research goals to the general public using only everyday language? (4) What if we can easily access brief news from other fields on a daily basis? How would the mathematical community be changed? You may think that these are strange questions, but system design has the potential to influence on everything. I’d like to list what the individual mathematicians can do for their academic freedom and diversity.

Discussion Theme (second part):

(i) 若手研究者が公平・公正な競争機会を得るために行われていること・あなたの構想、(ii) 数学者が研究のために行う（かもしれない）「泥臭い仕事」について、 (iii) 2024年の物理・化学ノーベル賞がAIの研究に与えられたので、社会に同様の社会的インパクトを与えるために数学が今できること。
(i) What is being done to ensure that young researchers have a fair and equitable opportunity to compete? And what is your vision for it?, (ii) About the "dirty work" that mathematicians (would) do for research, (iii) In light of the fact that the 2024 Nobel Prize in Physics and Chemistry was awarded to AI research, we would like to discuss what mathematics can do now to have a similar social impact on society.