a few accomplishments, two of them mathematical.

i felt quite proud of myself this weekend. among other things ..

1. I chose not to attend my usual Student Geometry Topology Seminar but instead dared the AIM Seminar (Applied & Industrial Mathematics) because I thought I would see a talk on wavelets; the abstract did say something about image segmentation, and it seems one of the usual suspects, after all.
   
   Instead, I was pleasantly surprised to see in action the spaces:
   
   
   • W^1,1₀ (the vanishing Sobolev space)
     
   • BMO (functions of bounded mean oscillation - they even cited work by J. Garnett and P.W. Jones, on dyadic stuff!)
     
   • BV (functions of bounded variation)
     
   • and their dual spaces
     
   • and order-1 distributions (i.e. the distributional divergences of functions from such spaces)
     
   It was like seeing old friends again, and more so than I mean. Whenever I see old friends, there is little time and it runs short: so it was with these nice function spaces. The speaker discussed them only in the last twenty minutes or so, and the talk ended late because of an excess of details. In the meanwhile, I wonder how many in the audience understood the context of these functions .. \:
2. I fled the country with friends and had a pleasant time in Windsor (the city in Canada across the river from Detroit), although I felt a little old, since the drinking age over there is 18 and the bars and clubs were full of young whippersnappers and other creatures of the night ..
   
   .. and despite that tempting environment, I did adhere to my axioms.
   
   
3. Most of all, last night I thought about a problem of my own, and I was able to solve it with a covering theorem!
   
   Granted, it wasn't the 5B-Covering Theorem (I don't work in spaces of that generality, usually) but Vitali's Covering Lemma in good old Rⁿ. I felt like something I learned actually stuck and was made useful .. as if my brain's cortex has been worth something, after all!
   
   Let's hope it remains a proof tonight, and wasn't the outcome of an overexcited mind. \: