A Functional Analysis of the Hypoelliptic Laplacian

亚椭圆拉普拉斯算子的泛函分析

• 批准号: DP230100434
• 负责人: Dr Dmitriy Zanin
• 金额: $ 29.25万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2023
• 资助国家: 澳大利亚
• 起止时间: 2023-01-01 至 2025-12-31
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP230100434
• 关键词: Functional; Analysis; Hypoelliptic; Laplacian

Strike a bell, a sphere, or any geometrical object, and it rings. The frequencies of ringing are the mathematical spectrum, which encodes deep secrets about the shape of the object. The spectrum of the hypoelliptic laplacian is known to carry deep truths in mathematics and physics, but it remains difficult to understand. We propose a new analytic foundation, which will replace the so far non-analytical ad hoc approach, and make accessible many new results. It is key to better understanding differential equations which lie at the boundary between quantum mechanics and the classical world. This will pave the way for Australian leadership in a new century of differential equations and geometry, and training of young mathematicians.

敲铃，一个球或任何几何物体，然后响。铃声的频率是数学频谱，它编码了有关对象形状的深度秘密。众所周知，低纤维化拉普拉斯的频谱在数学和物理学上具有深刻的真理，但仍然很难理解。我们提出了一个新的分析基础，该基础将取代到目前为止的非分析临时方法，并使许多新的结果可访问。更好地理解位于量子力学与古典世界之间边界的微分方程的关键。这将为澳大利亚的领导层铺平道路，在新世纪的微分方程和几何形状以及对年轻数学家的培训。