数論幾何学セミナー: Hilbert’s tenth problem and related topics

開催日時
2013年   3月 12日 10時 00分 ~ 2013年   3月 12日 17時 00分
場所
北海道大学理学部3号館413
講演者
萩原 啓 (北海道大学)
 
Abstract: The Diophantine equation is one of the most ancient and

inspiring branches in mathematics, and still promotes the development of

mathematics as well as number theory, as Fermat's Last Theorem did.

Concerning this important theme, in his lecture in 1900, Hilbert asked the

audience to find an algorithm that would determine whether a given

Diophantine equation has a solution. This question is placed on his famous

list of 23 problems, as the tenth problem.

After seventy years, Matiyasevich, building upon the previous work of

Davis, Putnam, and Robinson, showed that there exists no such algorithm.

While this theorem sounds negative, it actually yields several positive

by-products such as a prime-producing polynomial, and has opened a new

field of research, which is still full of unanswered questions.

In this talk, we will give a survey on their result with a brief review of

the notion of algorithm, and if time allows, discuss some topics related

to number theory and arithmetic geometry.

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関連項目

研究集会・セミナー・集中講義の一覧へ