Is the world smooth or non-smooth? Can mathematics tell us?

Abstract: In modeling different dynamical processes in physics, engineering, and the life sciences we often use models that have some kind of smoothness associated with their evolution. Meanwhile, models with abrupt changes – non-smoothness – have recently seen more frequent demand, application, and success. These contrasts raise a number of questions, such as, which type should we use? Are the non-smooth models driving new mathematics? Has our preference for certain types of mathematical properties kept us from considering certain types of models? We consider some non-smooth models on completely different scales, in the areas climate, energy transfer, and neural feedback, to see what these models can capture about the systems they describe. These examples also provide some perspectives about the mathematics that is needed and available for understanding and applying these models.

Mathematics

Audience: researchers in the topic

UCLA distinguished lecture series

Series comments: Description: Lectures by distinguished mathematicians, hosted at UCLA

Every year, the Distinguished Lecture Series (DLS) brings two to four eminent mathematicians to UCLA for a week or more to give a lecture series on their field, and to meet with faculty and graduate students.

The first lecture of each series is aimed at a general mathematical audience, and offers a rare opportunity to see the state of an area of mathematics from the perspective of one of its leaders. The remaining lectures in the series are usually more advanced, concerning recent developments in the area.