Probability

假设你知道一个物体的形状，你能计算出该物体的热扩散行为吗？反过来说，如果你知道一个物体的热扩散行为，你能推断出它的形状吗？物体的哪些几何特征对决定热扩散行为是真正重要的？物体形状的微小变化如何影响热扩散行为？这些基本问题及其变体将在拟议的研究计划中使用概率论和微分方程的思想进行探索。

Suppose that you are given the shape of an object, what can you calculate about the behaviour of heat diffusion of that object? Conversely, if you are given the behaviour of heat diffusion of an object, can you deduce some information about its shape? Which geometric features of the object are really essential to determine the behaviour of heat diffusion? How do small changes to the shape of an object affect the behaviour of heat diffusion? These fundamental questions and their variants will be explored in the proposed research program using ideas from probability theory and differential equations.