I am conducting research in number theory motivated by cryptography, with a particular focus on isogeny graphs. An isogeny graph is constructed from elliptic curves and isogenies between them. These graphs have rich mathematical structure and exhibit strong properties such as efficient diffusion of information across networks. In addition, it has been shown that hash functions can be constructed from isogeny graphs, highlighting their close connection to cryptography. I focus on the “number of cycles” in isogeny graphs. Investigating the number of cycles not only provides clues for understanding the overall structure and complexity of the graph but also leads to the analysis of properties such as how information propagates through the network. I am currently conducting research with the goal of deriving mathematical formulas that quantitatively provide the upper bounds on the number of such cycles.

Ever since I was in elementary school, I often read essays and popular science books about mathematics. Through these, I learned that mathematics is applied to everyday technologies, such as cryptography, which sparked my interest in the usefulness of mathematics. Later, when I was considering which laboratory to join for my fourth-year seminar, I consulted a professor about which laboratory I should join. I explained that while I was interested in algebra, particularly elliptic curves, I was also interested in applied mathematics. He then introduced me to elliptic curve cryptography. This experience led me to become interested in studying cryptographic theory related to elliptic curves.

Do you have things you want to do or a vision for your future? When I was in high school, I did not have a clear goal and spent a long time thinking about what field I should study, but I finally decided to follow what I liked and enrolled in the Department of Mathematics. Now, I am truly glad that I chose mathematics. Because it is something I love, I do not easily give up on it. For those who are still thinking about their future, I encourage you to turn your attention to something you truly enjoy and value. I also believe that connections with others are very important. Through interacting with people, I have gained new insights and feel that my perspective has broadened significantly. During my time at university, I have been supported by many people. I encourage you to value each encounter and to speak with all kinds of people.