Mathematical Study of Renormalization Groups and applications to Dynamical System

伊藤从多个角度研究了重整化群方法在数学科学中的应用。他从统计力学的角度对里奇流进行了研究，并提出里奇流对流形的变换与Pirogov-Sinai相变理论密切相关。他还重新考虑了Ya Sinai和D.Li i关于构造流体Navier-Stokes方程（复）湍流解的论文，采用了重整化群型论证。这篇论文似乎需要一些计算才能被理解。几十年前，伊东对夸克约束问题进行了研究，并在米格达尔-卡达诺夫型的层次近似中建立了约束。然而，出现了一篇误导性的论文，其中发件人声称他建立了监禁。伊藤和马克斯普朗克研究所的塞勒教授争论了他是如何以及为什么在他的论点中犯了错误。

Ito studied applications of renormalization group method in mathematical sciences from various points of view. He investigates the Ricci flows from statistical mechanics point of view, and suggested that the transformation of manifolds by the flow is strongly related to the Pirogov-Sinai theory of phase transitions.He also reconsidered the paper by Ya Sinai and D.Li on the constructions of (complex) turbulent solution of Navier-Stokes equation of fluid, using the renormalization group type argument. It seems that the paper needed some calculations to be understood. Ito studied quark confinement problem some decades ago, and established confinement in the hierarchical approximation of the Migdal-Kadanov type. However there appeared a misleading paper in which the author claimed that he established the confinement.Ito and Prof.E.Seiler of MaxPlanck Institute argued how and why he made mistakes in his arguments.