When dealing with gradient flows, did you ever wonder why it is better to choose a certain energy rather than another? And how the choice of energy influences the choice of metric and vice versa? Did you every ask yourself what a certain entropy or metric means in terms of modelling choice?
Well, I did, many times. And finally I came across these lecture notes by Mark Peletier who are very enjoyable to read , very understandable even for people with little background in gradient flows, and they also make the connection to the world of probability and large deviations. Enjoy!
PS: If you are keen to know the connection between gradient flows and the Poincaré conjecture, have a look at this blog post by Terence Tao. You may also get a glimpse at some of Perelman’s ideas that helped solve it.