Study of Geometry of a discrete space through randomness

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20244002
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Tohoku University
• Principal Investigator: KOTANI Motoko Tohoku University, 大学院・理学研究科, 教授 (50230024)
• Project Period (FY): 2008 – 2011
• Keywords: ランダムウォーク / ラプラシアン / 距離測度空間

Research Abstract

本研究では,幾何学と確率論の異なる分野の関わりを通じて,これまで扱えなかった離散空間の幾何解析学を新たに構築することを目的とする
初年度である平成20年度に大規模な国際研究集会を行い,連携研究者全員の知識と理解の共通基盤を確立する.それに従い,21年度には下記の具体的な問題に取り組む.22年度にはそれまでの成果を再検討し,必要な指針修正を行うことで,23年度への成果につなげる.4年間の研究を通して,離散幾何学の新たな研究手法を開発する

Research Products

• [Journal Article] A topological splitting theorem for weighted Alexandrov spaces (2011)
  • Author(s): T.Shioya, Kazuhiro Kuwae
  • Journal Title: Tohoku Math.J. 63 no.1 Pages: 59-76
  • Peer Reviewed
• [Journal Article] Asymptotic Euler-Maclaurin formula over lattice polytopes (2011)
  • Author(s): T.Tate
  • Journal Title: J.Funct.Anal. 260 no.2 Pages: 501-540
  • Peer Reviewed
• [Journal Article] Probabilistic Approach to Geometry (2010)
  • Author(s): Edited, M.Kotani, M.Hino, T.Kumagai
  • Journal Title: ASPM 157
  • Peer Reviewed
• [Journal Article] Diffusion on the scaling limit of the critical percolation cluster in the diamond hierarchical lattice. (2010)
  • Author(s): B.M.Hambly, T.Kumagai
  • Journal Title: Comm.Math.Phys. 295 Pages: 29-69
  • Peer Reviewed
• [Journal Article] Spectral Analysis in Geometry and Number Theory (2009)
  • Author(s): M.Kotani, H.Naito, T.Tate
  • Journal Title: Contemporary Mathematics (American Mathematical Society) 484
  • Peer Reviewed
• [Journal Article] Fixed-point property of random groups (2009)
  • Author(s): H.Izeki, T.Kondo, S.Nayatani
  • Journal Title: Annals of Global Analysis and Geometry 35 Pages: 363-379
  • Peer Reviewed
• [Presentation] Asymptotic Euler-Maclaurin expansion over Delzant polytopes (2010)
  • Author(s): Tatsuya Tate
  • Organizer: AMS-SMM 8th International Meeting at Berkeley
  • Place of Presentation: University of California, Berkeley
  • Year and Date: 2010-06-04
• [Presentation] Convergence of discrete Markov chains to jump processes and its application to random conductance models (2009)
  • Author(s): T.Kumagai
  • Organizer: Scaling Limits in Models of Statistical Mechanics
  • Place of Presentation: Oberwolfach
  • Year and Date: 2009-08-20
• [Presentation] Uniqueness of Brownian motion on Sierpinski carpets (2008)
  • Author(s): T.Kumagai
  • Organizer: Stochastic Analysis
  • Place of Presentation: Oberwolfach研究所(ドイツ)
  • Year and Date: 20080600
• [Presentation] Geometric analysis on Alexandrov spaces (2008)
  • Author(s): T.Shioya
  • Organizer: Sminaire Borel : New approaches to curvature
  • Place of Presentation: スイスレデイアブラレ
  • Year and Date: 2008-08-25
• [Book] ウェーブレット (2010)
  • Author(s): 新井仁之
  • Total Pages: 463+xi
  • Publisher: 共立出版