Shiro Goto (1946-2022)

We are deeply saddened to share with the community the news of the passing of Shiro Goto on July 26, 2022, at the age of 76. In accordance with the mind of the bereaved family, this announcement has been delayed.

Shiro Goto, courtesy of Kei-ichi Watanabe.

The following is a note we received from Ryo Takahashi:

“Shiro made important contributions to commutative algebra. His early works include the ones about the foundational theory of graded rings with Kei-ichi Watanabe and about the Eisenbud-Goto conjecture. He also deeply investigated the ring structure of blow-up algebras, and the integral closedness of ideals. His main interest in recent years was in establishing the theory of almost Gorenstein rings. He was also a great advisor of a lot of both formal and informal students. His passing is a big loss to our community.”

The following is a note we received from Kei-ichi Watanabe:

“Shiro Goto’s death has left a great void in my life. I had not met him since 2019 because of the covid pandemic, so I will always remember him as energetic and eager for mathematics. Indeed, as I heard from his younger friends, he talked about mathematics problems just a few days before he passed away.

I first met Goto in 1971, at a conference on commutative algebra in Yokohama. Those days Professor Nagata was in Kyoto, and Professor Matsumura was in Nagoya, and we, in Tokyo, had no teacher in commutative algebra. I was running a seminar with I. Kimura, S. Tachibana, and Y. Matsuura, and we agreed to invite Goto to that seminar. The invitation was successful after several tries, and ever since then Goto became a very important figure at the seminar.

The seminar met twice a week; we eagerly studied every interesting topic in commutative algebra in detail, hours at a time, as well as several topics in algebraic geometry. We did not know about our futures: I had a job of “Assistant” at that time, and it took a few years for Goto to get a degree and a job.

In this manner, Goto and I wrote up “On graded rings, I” and then “On affine semigroup rings” (with N. Suzuki), “The structure of one-dimensional F-pure rings,” etc. Also, Goto and I participated in the famous conference “Analytic Methods in Commutative Algebra” in 1979, at George Mason University. We traveled together, full of anxiety — this was our first travel outside Japan.

In 1978, Goto and I organized a symposium in commutative algebra; it later became known as “The 1st Japan Symposium on Commutative Algebra.” It has been organized annually by various commutative algebraists, with “The 43rd Japan Symposium on Commutative Algebra” planned for later this year.

In 1980 I left the seminar, moving to Nagoya Institute of Technology; the seminar was run by Goto at Nihon University, and later at Meiji University. The members of the seminar included Y. Shimoda, K. Yamagishi, K. Nishida, K. Kurano, Y. Nakamura, T. Kawasaki, and many others; the complete list would be far too long, but I should say that I myself have greatly benefitted from the “Goto Seminar.” The seminar began at 1:00 p.m. and speakers went through every detail of the proofs, while Goto and others raised many questions.

Every commutative algebraist knows Goto’s work. His theorems are very deep and sometimes unexpected; he thinks very deeply. He was really great as a mathematician, and also powerful as a teacher and an organizer. He sometimes said to me proudly, “this is how to nurture young students.” We, in Japan, have benefited from many international seminars organized by him. We will remember Goto and his work forever.”

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