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”指的是这门学科涉及微积分的扩展和概括（微积分是由牛顿和莱布尼茨发明的，用于研究行星的运动，通常被认为是科学上伟大的智力成就之一）。分析使人们能够以一种精确的方式确定数量是如何依赖于其他变量的，例如，地球卫星的速度如何随时间变化。一般来说，这种关系被称为数学函数。当然，可能存在“表现良好”的函数，例如卫星的速度，但也可能存在非常不受控制和剧烈波动的关系，例如股票市场上的股票价格随时间的变化。

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.