Algebraic and Geometric Approaches to Some Long-standing Problems of Analysis

我的研究兴趣是分析的一般领域。“分析”指的是微积分(由牛顿和莱布尼茨发明，用于研究行星运动，通常被称为科学的伟大智力成就之一)的推广和推广。通过分析，人们可以准确地确定量是如何依赖于其他变量的，例如，地球卫星的速度如何随着时间的推移而演变。一般而言，这种关系称为数学函数。当然，可能会有像卫星速度这样的“行为良好”的函数，但也可能有非常不受控制和剧烈波动的关系，比如股票市场上的股价随着时间的推移。

My research interests are in the general areas of Analysis. The ''Analysis'' refers to the fact the subject deals with extensions and generalizations of the Calculus (which was invented by Newton and Leibnitz to study the motion of the planets and is often referred to as one of the great intellectual achievements of Science). Analysis allows one to determine, in a precise manner, exactly how quantities depend on other variables, for example, how the velocity of an earth satellite evolves over time. In general, such relationships are called mathematical functions. Of course, there may be ''well-behaved'' functions such as the velocity of a satellite, but there may also be very uncontrolled and wildly fluctuating relationships, such as the price of a share on the stock market over time.