The First Threads

I have been pondering what to write about, and now it is time to get on with it. In the end, I am really writing for myself rather than for any larger readership, so I am going to just pick some things I want to learn and get going. I have settled on two topics for the upcoming semester:

1. An Example A Day for my differential geometry class. I really mean an example for each class meeting, so there should be about forty of these posts in the next four months. I intend to pick some classical curves and surfaces with beautiful properties and share them.
2. Some classical differential geometry theorems. As always, there is more math out there than I have learned, and teaching a class is a good excuse to add to the depth of my knowledge. I will try to pick out some interesting theorems from the early days of differential geometry (before tensors, before the dark times), learn them and their original arguments, and write them up.
3. The Gage-Hamilton theory of curve shortening flow, and related geometric analysis questions.

Topics 1 and 2 come from a the teaching I will be doing this term, and topic 3 is related to some undergraduate research projects I am mentoring now and planning to mentor next year.

Read along if it appeals to you. Eventually some of these strains will die out and I will pick up something else.