## Associate Prof. Takeshi Tsuji is awarded the 5th Japan Academy Medal

Associate Professor Takeshi Tsuji

Associate Prof. Takeshi Tsuji received the 5^{th} Japan Academy Medal and the 5^{th} JSPS Prize for his achievements in p-adic Hodge theory and its applications, which is a branch of number theory. The JSPS Prize is a prize given by JSPS (Japan Society for the Promotion of Science) to recognize young researchers who are advancing excellent researches. Among the JSPS Prize recipients, the Japan Academy Medal recipient is selected.

Number theory is a field of mathematics in which the mysteries of the world of integers 0, 1, 2, … are studied. This explanation could make it sound like a simple theory but it is only the way it looks. There is a huge gap between its appearance and actual difficulty it contains. Study on number theory has a long history and its significant progress in recent years is spectacular. The source of this progress is the discovery of the world of p-adic number around 100 years ago. By considering integers not only as real numbers but also as p-adic numbers associated to each prime number p=2, 3, 5, …, the number theory has made major advances.

Prof. Tsuji received the prizes for completing a theory that captures geometric objects in the world of p-adic numbers. When the method called cohomology is applied, geometrically curved objects can be studied by means of linear-algebraically straight ones. Thanks to Prof. Tsuji's achievement, a theory that runs parallel to cohomology theory known as the Hodge theory in the world of complex numbers has been completed in the world of p-adic numbers. This p-adic Hodge theory is directly linked to the naive world of integers via Galois theory and has made a wide range of applications possible in number theory.