Kazuya Kato
Encyclopedia
is a Japanese mathematician. He grew up in the prefecture of Wakayama in Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...

. He attended college at the University of Tokyo
University of Tokyo
, abbreviated as , is a major research university located in Tokyo, Japan. The University has 10 faculties with a total of around 30,000 students, 2,100 of whom are foreign. Its five campuses are in Hongō, Komaba, Kashiwa, Shirokane and Nakano. It is considered to be the most prestigious university...

, from which he also obtained his master's degree in 1975, and his PhD in 1980. He was a professor at Tokyo University, Tokyo Institute of Technology
Tokyo Institute of Technology
The Tokyo Institute of Technology is a public research university located in Greater Tokyo Area, Japan. Tokyo Tech is the largest institution for higher education in Japan dedicated to science and technology. Tokyo Tech enrolled 4,850 undergaraduates and 5006 graduate students for 2009-2010...

 and Kyoto University
Kyoto University
, or is a national university located in Kyoto, Japan. It is the second oldest Japanese university, and formerly one of Japan's Imperial Universities.- History :...

. He joined the faculty of the University of Chicago in 2009.

He has fundamentally contributed to many parts of modern number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...

 and related parts of algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...

. His first work was in the higher-dimensional generalisations of local class field theory using Milnor K-theory. It was then extended to higher global class field theory in which several of his papers were written jointly with Shuji Saito. He contributed to p-adic Hodge theory
P-adic Hodge theory
In mathematics, p-adic Hodge theory is a theory that provides a way to classify and study p-adic Galois representations of characteristic 0 local fields with residual characteristic p . The theory has its beginnings in Jean-Pierre Serre and John Tate's study of Tate modules of abelian varieties and...

, logarithmic geometry (he was one of its creators together with Jean-Marc Fontaine and Luc Illusie
Luc Illusie
Luc Illusie is a French mathematician. He is a former student of École Normale Supérieure, and got his PhD under the supervision of Alexander Grothendieck. He is professor emeritus at the Paris-Sud 11 University. Illusie made notable contributions to algebraic geometry.-External links:*...

), comparison conjectures, special values of zeta functions including the Birch-Swinnerton-Dyer conjecture and Bloch-Kato conjecture on Tamagawa numbers, Iwasawa theory
Iwasawa theory
In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa, in the 1950s, as part of the theory of cyclotomic fields. In the early 1970s, Barry Mazur...

, and many others.

A special volume of Documenta Mathematica was published in honor of his 50th birthday.

Together with research papers written by leading number theorists and former students it contains Kato's song on Prime Numbers.
In 2005 Kato received the Imperial Prize of the Japan Academy
Imperial Prize of the Japan Academy
The was a prestigious honor conferred by the Imperial Academy from 1911 through 1945. The award was presented to non-members in recognition of their academic theses, books, and achievements....

 for "Research on Arithmetic Geometry".

Books

He published many books in Japanese, of which several have already been translated into English. He wrote a book on Fermat's last theorem
Fermat's Last Theorem
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....

and is also the author of the two volumes of the trilogy on Number Theory, of which the first two have been translated into English.
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