Group actions in function approximation spaces

1987年，英国经历了一场著名的飓风，这场飓风是英国气象局没有预测到的。PI听说，在气象局工作的数学家们经过适当的考虑后决定，原因是用于预测极端天气的数字代码有一个特别细微的缺陷：计算机代码中没有内置一个被称为势涡度的守恒定律。这种守恒定律是由著名的定理保证的，该定理由艾米·诺特在1900年初由S证明，该定理将物理模型的对称性直接与守恒定律联系起来。该项目研究方向的长期目标是建立这样的定律，确切地说，是对物理系统进行建模的数字代码。这包括首先理解物理对称如何被映射到离散或数字空间中的动作；实际上，映射到用于模拟光滑函数的此类空间上的近似函数。第二部分具体而实用地研究了Noether定理如何转化为离散情形。

In 1987, Britain experienced a hurricane that was famously not predicted by the UK Met Office.The PI heard that mathematicians working at the Met Office decided, after due deliberation, that the reason was that the numerical code used to predict extreme weather had a particular subtle flaw: that a conservation law, known as potential vorticity, was not built into the computer code. This kind of conservation law is guaranteed by a famous theorem, proved by Emmy Noether in the early 1900's, which links the symmetries of the physical model directly to the conservation laws.The long term aim of the line of research of the project is to build such laws, exactly, intonumerical code that models physical systems. This involves first understanding how the physical symmetries, which are understood in terms of smooth actions on smooth spaces,are mapped into actions in discrete or digital spaces; actually, onto the approximate functions on such spaces used to model the smooth functions. The second part involves investigatinghow Noether's theorem transfers to the discrete case in a concrete and practical way.