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

(04 octobre 2024/October 04, 2024) Série de conférences de la Chaire Aisenstadt.
www.crmath.ca/...
Colloque des sciences mathématiques du Québec/CSMQ
Rachel Kuske (Georgia Institute of Technology): 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 seen more frequent application, success, and necessity. These changes raise a number of questions, such as, which should we use? Are the non-smooth models driving new mathematics, or 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 also provide some perspectives about the mathematics needed and available in understanding and applying these models