Measure-valued and Partition-valued Processes and Random Matrices

首席研究员埃文斯研究进化的生物种群的随机模型，在这些模型中，个体与彼此及其环境相互作用。他研究了聚合、凝聚和缩合的物理和化学模型中出现的聚合树过程，以及种群遗传学中的垫脚石模型的研究。他提出了一种新的方法，利用对称马尔可夫过程理论来研究粒子物理学中出现的大型随机矩阵和数论中的某些猜想。他提出了一系列起源于随机微分几何的模型，用于生物种群中遗传类型的进化。首席研究员的不同方面的工作使我们更好地理解了：大种群中进化的基因图谱的动力学，随着时间的推移，单位聚集在一起形成更大单位的一般物理过程，以及粒子物理中的一类模型，这些模型不仅成功地解释了一系列广泛的实验结果，而且与其他一些看似无关的数学领域有着深刻的联系。

0071468Evans The principal investigator studies stochastic models for evolving biological populations in which individuals interact with each other and their environment. He investigates coalescing tree processes that arise in both physical and chemical models of polymerisation, coagulation, and condensation, and in the study of stepping-stone models in population genetics. He suggests a new approach using the theory of symmetric Markov processes to the study of large random matrices that appear in particle physics and certain conjectures in number theory. He proposes a family of models originating in stochastic differential geometry for the evolution of genetic types in biological populations. The various strands of the principal investigator's work lead to a greater understanding of: the dynamics of evolving genetic profiles in large populations, general physical processes in which units clump together over time to form larger units, and a class of models in particle physics that have not only successfully explained a wide array of experimental results but also have deep connections with a number of other seemingly unrelated areas of mathematics.