### Which high school and university did you graduate from?

I attended Ishikawa Prefectural Komatsu High School. I graduated from Kyoto University with a 4-year undergraduate degree and a 2-year master’s degree and completed a 3-year doctoral degree from the University of Tsukuba.

### What first made you decide to become a mathematician?

Even as a child, I had vague aspirations to become a researcher. My preferred subjects were always arithmetic and mathematics, so my first priority, at that time, was to become a mathematician. I seriously considered a career in mathematics for the first time during my master’s course. I wanted to be a mathematician, but I was a little apprehensive about my potential to enter the doctoral course and whether I would be able to handle the course (not being the most outstanding student!); I was fairly troubled about my career options. However, the studies I was pursuing toward my master’s thesis were so interesting that I wanted to investigate them further; I decided to stop seeking employment and instead embarked on a doctoral course.

### Please explain the details of your research.

My research belongs to a field called “combinatorial representation theory.” The aim was “to convert a problem in representation theory to a problem in combinatorics.” Representation theory is a major field in mathematics, which developed from attempts to express abstract and intractable subjects such as groups and rings, studied in the second and third years of the undergraduate course, in a more understandable matrix representation. My research focuses on “representation theory of Lie algebras and quantum groups,” which is closely allied to various aspects of physics, chemistry, and mathematics and has evolved into an extremely important and interesting field (*the following website is an excellent reference on representation theory:

Web Server of Representation Theory (JP)). On the other hand, combinatorics counts the number of items that satisfy given conditions. For example, a typical problem in high school mathematics, “in how many ways can 2 items be selected out of 10?”, can be considered a combinatorial problem. An example of the type of problem appearing in my research is given below:

Problem: Align several cells as shown in the diagram below such that the number of cells in a row is equal to or less than the one in the preceding row, proceeding from top to bottom and aligned left. For n number of cells (n = 25 in the diagram below), enter numerals in the cells from 1 to n by following the rules listed below:

1) For each individual cell, if that cell has a neighbor to the right, the neighbor is assigned a number greater than that assigned to the individual cell.

2) For each individual cell, if that cell has a neighbor below it, the neighbor is assigned a number greater than that assigned to the individual cell.

In how many ways can these numbers be filled?

### What kind of knowledge is required?

Various research styles are adopted in representation theory, but the research in my laboratory requires linear algebra (matrix theory) and basic algebra. I believe that other topics can be studied as required. In combinatorics, advanced knowledge is frequently less important than ideas and imagination. Solving a problem in combinatorics is like solving a puzzle.

### What do you think are the special features of mathematics at the University of Tsukuba?

The mathematics department at the University of Tsukuba employs several teaching staff researching various fields. A particular feature of this University is the presence of teaching staff in information fields, such as mathematical statistics, mathematical logic, and computational mathematics. I believe that very few universities employ staff in these fields. Another feature of the University of Tsukuba, especially as it was formerly the Tokyo University of Education, is that many of its students aspire to become high school or junior high school teachers.

### How many students are in charge?

As of April 2012, one student is enrolled in the doctoral program and four students are pursuing research for their thesis project.

### Where have previous students found employment?

Five years ago, I was responsible for overseeing thesis projects for five students. Two of the students became teachers, one joined a publishing company related to education, and the other two proceeded to the Graduate School of Education at the University of Tsukuba. The single student who completed the master’s program in 2011 is now a high school teacher.

### What are your interests outside mathematics?

Reading books -- I enjoy mystery novels and comics -- playing games, and jogging -- there is a good jogging course in the University of Tsukuba campus. I am probably not too different from the students (laughter).

### Finally, could you give us a message for our readers?

Anyone with a passion for mathematics (whether mathematically talented or not) should try studying mathematics at the university level. I’ll be waiting for you at the University of Tsukuba!