Mathematical approach to materials science by using non-commutative geometry

2014 Fiscal Year Final Research Report

• Project/Area Number: 23654020
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Tohoku University
• Principal Investigator: KOTANI Motoko 東北大学, 理学(系)研究科(研究院), 教授 (50230024)
• Co-Investigator(Renkei-kenkyūsha): AKAMA Yohji 東北大学, 大学院理学研究科, 准教授 (30272454) ; ODA Tadao 東北大学, 大学院理学研究科, 名誉教授 (60022555)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 非可換幾何学 / 準結晶 / 格子欠陥 / 量子ホール効果

Outline of Final Research Achievements

One of the fundamental questions of solid state physics is to understand relations between microscopic structures and macroscopic properties of matter. One can computer properties in principle if the matter assumes periodic structure. It however often happens that periodic structures are broken under various physical environment such as with impieties, magnetic fields, boundaries. In this project we challenge to establish a new mathematical approach to those problems by using non-commutative geometry.

Free Research Field

幾何学、離散幾何解析学