The calculus of variations began with Newton's study on minimal resistance. In the following few centuries, the calculus of variations has achieved fruitful developments and applications in different science fields, including geometry, physics, and engineering etc. I plan to start the discussion with the extremal problem of smooth functions, then extend to the first and second variation in functional analysis. Depending on the remaining time, concrete examples to be discussed might include the following geometric objects: hanging chain, geodesics, minimal surfaces, harmonic maps, Yang-Mills connections. From these examples, I hope to unveil the possible complexity of extreme objects.

Speaker

A/Prof. Langte Ma

School of Mathematical Science, SJTU

Time

 2025.12.3 12:00-13:30