Mayuko Yamashita
Associate Professor
Department of Mathematics, Kyoto University
Japan
Asian Scientist Magazine (Dec. 21, 2023) —When people think of mathematics and physics together, it’s often about applied mathematics enabling something practical, such as engineering. However, there is a deep connection between pure mathematics and fundamental physics. Japanese mathematician Mayuko Yamashita is passionate about exploring this connection.
At 28, Yamashita is an associate professor at Kyoto University’s Graduate School of Science. In 2022, she won the inaugural Marie Sklodowska Curie Award for emerging Japanese female researchers. In September 2023, Yamashita was awarded the Maryam Mirzakhani New Frontiers Prize by the Breakthrough Foundation. The award celebrates her work in index theory and mathematical physics.
Broadly speaking, index theory deals with how the topology of a space relates to the behavior of objects in it. It allows mathematicians to study the properties of mathematical objects — numbers, functions, or shapes — and how they’re connected to physical objects.
For physicists, it provides a tool to tease out the hidden mathematics behind concepts like quantum field theory (that explains how subatomic particles move and interact) and string theory. While string theory posits that the universe is made up of infinitesimally small vibrating strings, index theory offers a window into the properties of these strings in the absence of experimental evidence. Yamashita is one of the upcoming mathematicians ensuring that physicists are best equipped to make use of this tool. Yamashita speaks to Asian Scientist Magazine about her journey into mathematical physics.
1. How did you decide a make a career in mathematics?
I was interested in mathematics from junior high school. I participated in the International Mathematical Olympiad. I gradually got interested in the theoretical aspects of modern mathematics by communicating with some senior university students and doctoral students. When I entered the undergraduate program, I thought that I liked mathematics but maybe I was not suited for doing mathematical research. I chose engineering but later I realized I liked mathematics more.
2. What is index theory and what are you working on?
Roughly speaking, mathematics consists of analysis, geometry, and algebra. Index theory provides a bridge between analysis and geometry. I am currently interested in its applications in mathematical physics. Index theory, in pure mathematics, is an old subject but recently it has become important in theoretical physics like topological matter [materials whose properties are determined by their geometry rather than their chemistry] and quantum field theory.
3. How do you see your work advance our understanding of physics?
While these are problems from many decades ago, the search for a mathematical understanding of these theories [for example string theory and quantum field theory] continues. We are working on the anomalies in string theory [unexpected phenomena that show up in theoretical models]. We also want to understand quantum field theory in a purely mathematical way. There are many formulations of quantum field theory which are supposed to be somewhat related. In the long run, I hope our work and related works contribute to finding those relations.
4. What’s a major challenge you face in your work and how do you overcome it?
Working on string theory requires a deep understanding of physics. I am trying to understand physics from the literature but it is still difficult for me as a mathematician. I learned mathematics first and my brain is mathematically oriented. It is difficult to understand a physicist’s intuition. I have collaborators who are physicists and they teach me. They try to translate their theories into mathematical language as much as they can. That benefits me.
5. What advice would you give to kids who are interested in mathematics?
My advice is to pursue what you want to do. I gave up mathematics once because I wasn’t confident enough, but eventually, I came to realize that it is best to do what I want to do. In mathematics and life, please don’t restrict yourself, and don’t be afraid of stepping into new areas.
(Responses have been edited for length and clarity.)
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This article is from a regular series called Asia’s Rising Scientists. Click here to read other articles in the series.
Copyright: Asian Scientist Magazine; Image: Yipei Lieu / Asian Scientist Magazine
