I gave a talk at the Working Seminar in Geometry and Analysis a couple of weeks ago and have now written up and posted the notes for the talk.

Abstract: A sub-Riemannian manifold models constrained motion through a choice of a "horizontal distribution" on the tangent bundle. The standard denitions of tangent space and the dierential of a smooth map break down in this setting. Following papers by Bellaiche and Ponge, I will discuss the way these notions are replaced by talking about non-abelian vector spaces (Carnot groups) and induced maps between them.

Ingredients:

1 cup sugar
1 3/4 cups flour
2 tsp baking powder
4 Tbsp butter
1 egg, slightly beaten
1/2 cup milk
1 Tbsp sugar mixed with 1 tsp cinnamon

Instructions:

Preheat oven to 375 F.
Mix sugar, flour, baking powder, then use fingers to mix in butter.
Add egg and milk and mix up.
Put into 8 inch square pan (buttered) and sprinkle with mixture. 
Bake for 20 minutes.

Quantum Field Theory: A Tourist Guide for Mathematicians, by Folland.

While in Germany, I talked to Herr Professor Doctor Zeppenfield, and he told me that quantum field theory accounts for much of modern physics. So when I saw Folland's book at the library (near a book I was looking for), I was intrigued. Folland says "[the subtitle] is meant to free me and my readers from guilt about omitting various important but technical topics, viewing others from a point of view that physicists may find perverse, ..., and skipping the gruesome details of certain necessary but boring calculations". What can be better?

Read more...

Our trip to Germany went very well, and we're now back in Urbana, working hard on grad student stuff. Cindy is still taking classes, working in the linguistics lab, and designing experiments of her own. I've been mostly auditing classes (3 registered, 1 not) and teaching Calc 3, which is a lot of fun, for all that I start teaching at 8am on TuTh. I've also been reading up on some physics - hopefully that'll help me steer properly towards the applied side of math.

As far as video of Germany... I now have a camera that shoots in full HD (thanks, mom & dad!) and I have about 6 hours' worth of Germany recorded. I cut this down to about an hour, and put the compressed version online. Unfortunately, the internet is not ready for 12gig/hour movies to be easily uploaded to a server, so I had to limit myself to ~1 gig of data, which really cuts down on the quality. Let me know if you want to see it in HD, and I'll mail you an SD card with the movie.

We also have lots of photos, and I'll put those up with a description within a couple of days.