Nippon Foundation Dwango Gakuen Preparatory Committee
The winning paper of the “1st IUT Innovator Award” has been decided. 100,000 USD will be presented by IUGC (Interuniversal Geometry Center) ……
The Nippon Foundation Dwango Gakuen Preparatory Committee has been working with the Center for Interuniversal Geometry, a research institution of the online university “ZEN University” (tentative name, applying for approval for establishment), which is currently applying for approval with the aim of opening in April 2025. The
Inter-universal Geometry Center (IUGC, Director: Fumimoto Kato) has decided the winning paper for the “1st IUT Innovator Award,” an award for papers related to IUT theory.
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The IUT Innovator Award aims to encourage the development of research related to IUT theory and the research activities of the younger generation.The IUT Innovator Award will be awarded to the best paper containing new and important developments in IUT theory and related fields every year for 10 years starting in 2024. , which will award prizes ranging from $20,000 to $100,000. The 1st IUT Innovator Award will be awarded to the following papers after a rigorous review by a panel of experts commissioned by the IUGC (Universal Geometry Center). “Explicit estimates in inter-universal Teichmüller theory”,
by Shinichi Mochizuki, Ivan Fesenko, Yuichiro Hoshi, Arata Minamide, Wojciech Porowski, published in Kodai Math. J. 45 (2022), pp.175-236 Shinichi Mochizuki, Yuichiro Hoshi, Arata Minamide, and Wojciech Porowski of the Institute for Mathematical Sciences, Kyoto University, who wrote the winning paper, will receive a cash prize of US$100,000 from the IUGC (Ivan Fesenko will receive the prize) (declined to accept).
Mr. Mochizuki and his colleagues hope to donate the prize money to the Kyoto University Institute for Mathematical Analysis as funds to support research activities related to interuniversal Teichmuller theory and related far-Abelian geometry. It has been.
-Introduction of the award-winning paper- The paper that won this award includes a strong version of Shinichi Mochizuki’s Interuniversal Teichmuller (IUT) theory. By applying this powerful version, for the first time in the history of mathematics, we succeeded in proving several effective abc inequalities expressed using explicitly specified constants.
The first application of the effective version of the abc inequality proven in this paper is a new proof of “Fermat’s Last Theorem,” one of the most famous theorems in mathematics. The proof uses one of the effective versions of the abc inequality and a lower bound of possible natural number solutions to the Fermat equation recently obtained by P. Mihailescu through more classical number theory arguments and some computer verification. There is.
The award-winning paper shows that integer solutions to various types of equations with integer coefficients can be solved by using more classical number theory to derive lower bounds of possible solutions and then applying the effective abc inequality. Now I can research this style. This is called Diophantine geometry, and it fundamentally changes the ancient research method of number theory.
Award-winning paper author:
Shinichi Mochizuki: Professor, Institute for Mathematical Sciences, Kyoto University
Ivan Fesenko: Special Invited Professor at West Lake University (China), Deputy Director of IUGC
Yuichiro Hoshi: Associate Professor, Institute for Mathematical Sciences, Kyoto University
Arata Minami: Special Assistant Professor, Institute for Mathematical Sciences, Kyoto University
Wojciech Porowski: Special Assistant Professor, Institute for Mathematical Sciences, Kyoto University
■ About IUT Innovator Prize and IUT Challenger Prize
At IUGC, with the aim of promoting the spread and development of IUT theory (Inter-universal Teichmüller Theory) by Professor Shinichi Mochizuki of the Institute for Mathematical Sciences, Kyoto
University, the IUT Innovator Prize and IUT Challenger Prize are awarded for papers related to IUT theory. was founded.
The IUT Innovator Prize is open to papers that include important new developments in IUT theory and related fields, and awards prizes ranging from $20,000 to $100,000 each year to the winner of the best paper.
In addition, the “IUT Challenger Prize” was established as an award by Dwango founder Masao Kawakami (individual). The $1 million prize is awarded to the first mathematician to write a paper on IUT theory that shows an essential flaw in the theory.
-Background to the establishment of the award- The official name of IUT theory is Inter-universal Teichmüller Theory, or Interuniversal Teichmüller Theory in Japanese. It was announced in Using the IUT theory, the abc conjecture, which is said to be “the most difficult unsolved problem” in the field of mathematical theory that deals with integers, can be solved, which has caused a great debate in the mathematical world since its announcement, and has been under review for seven and a half years. Later, in 2021, it was published in the international journal “PRIMS” edited by the Institute for Mathematical Sciences, Kyoto University. Meanwhile, there is an extremely unusual confusion in the mathematical world regarding the IUT theory, and while there are mathematicians who are skeptical about whether the theory is correct, there is no mathematical discussion on whether it is correct or not. The condition continues. Despite the importance of theory, one of the main reasons for this situation is that Professor Mochizuki’s theory is not only huge but also highly unique, and it takes a great mathematician to understand the claims of the IUT theory. Even so, it requires a lot of time and effort. The above award has been established to reward the hard work of mathematicians who are committed to IUT theory. I hope that this trial will increase the number of mathematicians who learn about IUT theory.
-Judging method for the IUT Innovator Prize- Every year for 10 years starting in 2024, we will select one paper that contains important new developments in IUT theory and related fields. The IUGC will manage and judge the IUT Innovator Prize and decide on the winning papers. ➢ Subject to review: Papers that have already been submitted to mathematics journals and submitted through self-recommendation or peer recommendation, and which present new versions or applications of IUT theory, new analyzes of the logical structure of the theory, or important contributions in areas closely related to these. Including. ➢ The amount of the award will be determined depending on the novelty of the paper and the importance of the contribution. ➢ Submitted papers will be evaluated by a closed review by a group of IUT theory experts appointed by the IUGC, independent of peer review in the specialized journal to which they are submitted. The evaluation results will be determined and announced by the IUGC. -Judging method for the IUT Challenger Prize- Judging will be conducted by Masao Kawakami based on his own individual judgment. The screening method will not be made public, but the papers to be screened will be from mathematics specialties that are listed on “MathSciNet” and where 10 or more papers on number theory and geometry have been published in the past 10 years. Only those that have been peer-reviewed and published in journals are eligible.
ZEN University Website▶https://zen-univ.jp
IUGC website▶https://zen-univ.jp/iugc
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