Topics in stochastic analysis: branching diffusion, reaction-diffusion equations, epidemiology, scintillation counters and insurance

我们提出了一个试点项目，目的是启动跨学科的讨论和未来的贡献，从数学系和医学院的成员。该项目包括一个广泛的主题列表有关的概率方法的应用到研究的反应扩散方程和模型的流行病学。这些主题中的许多可以发展成具有自己议程的单独项目。在本项目的框架下，我们将得到与黎曼流形上的分支扩散和大偏差有关的新的数学结果.此外，我们计划在HPC设施上进行流行病学模型的初步数值研究/模拟。该项目将导致空间流行病模型的系统研究，并包括一些核物理和保险的统计主题。

We propose a pilot project with the purpose to initiate the interdisciplinary discussions andfuture contributions from members of Department of Mathematics and School of Medicine.The project includes a wide list of topics related to the application of probabilistic methods tothe study of reaction-diffusion equations and models of epidemiology. Many of these topicscould be developed into separate projects with their own agenda. In the framework of thecurrent project new mathematical results related to branching diffusions on Riemannian manifolds and Large Deviations will be obtained. Also we plan preliminary numerical studies/simulation of epidemiology models on HPC facility. This project will lead to the systematic studyof spatial epidemic models and includes some statistical topics from nuclear physics andinsurance.