Is the World Smooth or Non-smooth? Mathematical Models in Dynamic Systems

Watch this hour-long Aisenstadt Chair lecture exploring the fundamental question of whether mathematical models should prioritize smooth or non-smooth approaches when describing real-world phenomena. Delve into how different modeling techniques handle abrupt changes versus continuous evolution across physics, engineering, and life sciences applications. Examine specific case studies in climate science, energy transfer, and neural feedback to understand the implications of choosing smooth versus non-smooth mathematical frameworks. Learn about the mathematical tools available for understanding these different modeling approaches and consider how historical preferences for certain mathematical properties may have influenced model selection. Gain insights into when non-smooth models might better capture system behavior and the new mathematical developments driven by these modeling needs.