Local geometry of real and complex analytic mappings

我的工作是在解析几何和交换代数的接口，现代数学的两个主要分支与应用在科学和工程。他们处理的分析多项式和解析函数和几何的空间上，他们的生活。我目前的研究课题是研究映射的局部退化。这种微小的退化可以完全破坏由映射定义的对象的几何规则性，因此知道如何检测它们是重要的。我的程序的主要任务是建立简单的代数准则来控制映射的局部行为。这项研究为研究生和博士后研究员的培训提供了机会，并涉及与其他数学家的国际合作。

My work is at the interface of analytic geometry and commutative algebra, two major branches of modern mathematics with applications in science and engineering. They deal with the analysis of polynomial and analytic functions and the geometry of the spaces on which they live. The subject of my current research program is the study of the local degeneracies in mappings. Such minute degeneracies can completely destroy the geometric regularity of the objects defined by the mappings, and hence it is important to know how to detect them. The main task of my program is to establish simple algebraic criteria to control the local behaviour of a mapping. This research provides opportunities for the training of graduate students and postdoctoral fellows and involves international collaboration with other mathematicians.