Construction, singularities and porlarlization of moduli space of metric spaces via Quantum statistical mechanics

2017 Fiscal Year Final Research Report

• Project/Area Number: 26610017
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Kyushu University
• Principal Investigator: OTSU Yukio 九州大学, 数理学研究院, 准教授 (80233170)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: Differential geometry / モジュライ空間 / Gromov-Hausdorff 距離 / 量子統計力学

Outline of Final Research Achievements

By the method of random discretization we considered the discrete Laplacian of nets on a compact Riemannian manifold or Alexandorv space. Using the Laplacian we constructed the Hamiltonian ofvibrations on net and its quantum statistical mechanics. By perturbation expansion of its thermodynamical functions we introduced a family of the Riemannian metrics on the bulk moduli space of the pairs of space and net. Then we studied its relation to the Gromov-Hausdorff distance and several classical moduli spaces.

Free Research Field

Differential geometry