Mathematics, Economics and Physics

数学、经济学和物理

• 批准号: 1000233080-2019
• 负责人: McCann, Robert
• 金额: $ 10.93万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=696084
• 关键词: Mathematics; Economics; Physics

This proposal aims to develop new mathematical tools from optimal transportation and variational calculus, to analyze key models from physics, geometry, and economics. Its goals include (i) understanding the structure or absence of singularities in optimal maps between given pairs of mass distributions, including those on spaces of unequal dimension; (ii) the analysis of pattern formation in nonlinear nonlocal models for various physical, biological and economic processes; and (iii) recasting Einstein's theory of gravity into a nonsmooth framework, which facilitates studying the limiting geometry of sequences of spacetimes and provides a new setting for exploring possible singularities among other phenomena.

这项建议旨在从最优运输和变分中开发新的数学工具，从物理学、几何学和经济学的角度分析关键模型。它的目标包括：(I)了解给定质量分布对之间的最优映射中奇点的结构或不存在；(Ii)分析各种物理、生物和经济过程的非线性非局部模型中的图案形成；以及(Iii)将爱因斯坦的引力理论重塑到非光滑框架中，这有助于研究时空序列的极限几何，并为探索可能的奇点以及其他现象提供了一个新的背景。