I was at the SIAM Annual Meeting in Portland from Tuesday through today (Friday). However, I've had relatively little time accessing, and I've spent more time on the human sort of networking than on the computer sort. I'll catch up on e-mail and such over the next few days.

The technical program was interesting. Topics that I found particularly exciting included:

• Shear wave imaging

  When a doctor feels for lumps, she moves her fingers back and forth. A lump is a place where the subsurface tissue is more resistant to the shearing force that comes from rubbing across the surface. We already use ultrasound imaging, which involves compression waves traveling through tissue. Why not use the much more slowly-traveling shear waves, too?

• Splines and Boeing

  There was a keynote talk about computations done at Boeing using spline. The talk involved a lot of pretty pictures, and also a back of the envelope calculation in which the speaker estimated that there were probably about half a billion spline calculations done in Boeing systems every day.

  A half billion is a lot.

• Equation-free and multiscale models

  Mathematical modeling usually involves creatively fuzzy vision. If you want to model a weight hanging on a spring, you can try to model every atom in the system, and go nuts; you can do some averaging and model the spring by a set of partial differential equations, and keep people like me employed; or you can assume that the amount that the string stretches is roughly proportional to the amount of weight you hand on an end, do one experiment to find the constant of proportionality, and go for a walk.

  We have a lot of tools, both analytical and numerical, that work well for systems described by partial differential equations. But what about systems of particle interactions in which we're not smart enough to write down a continuous approximation? It turns out that it's sometimes enough to posit such an equation exists (and is continuous) -- without writing it down. You use your microscopic model to fill in what's happening in a few places, and then use the data at those points to fill in everywhere else. The idea is simple, the details are hard, and the whole effort is immensely interesting.

  It's also sort of astounding. How do you solve an equation without the equation? Equation-free modeling sounds like it ought to be the title of a Zen koan -- if Zen koans had titles and a flair for the technical -- but it was actually the title for one of the keynotes.

  A related area, less magical-sounding but equally profound, is multi-scale modeling. It's exactly what it sounds like: there are some things that happen very quickly and some things very fast, or there are some things that happen over a large area and some over a small area. If you looked at everything finely enough, you'd see the whole picture, but that's unbearably expensive. So you selectively put on glasses, and build some machinery to connect the very small to the very large.

• Implicit codes and software engineering

  We didn't want to tell the scientists they would have to change their codes a lot. The scientists hate that.

  Very true. I'm glad to see it recognized.

• Google

  We'll take Google as an example. Nobody knows quite what Google does, but we think it might be this.

  Web searching is a hard technical problem involving some very interesting ideas from numerical linear algebra. Marveling at the math is almost as much fun as marveling at Google.

• Eigenvalue problems

  I talked about one type of eigenvalue problem. Other people talked about different types of eigenvalue problems. I enjoyed the talks and the conversations.

More generally:

• Portland is impressive. There is a book store here that covers an entire city block, and a companion technical book store which is also extensive. Several of us went there this afternoon; we met others with the same idea. We should have just held the last session here.
• There are other impressive things about Portland, too, like the train system and the people. And did I mention the book store?
• Through Thursday, there were vendor booths with several major technical publishers and a handful of people selling software. I bought two books, a little monograph on Lanczos algorithms and Matrix Algorithms, Volume II: Eigensystems by Pete Stewart. I've intended to buy the latter since it came out -- a year ago? two? -- and I haven't finished gloating over it yet.
• I still find it astounding to watch human networks at work. I met a lot of people at the meeting -- that's much of the point, after all. Some of them I knew from reputation, some of them I didn't. In any case it usually took all of fifteen seconds of conversations to find someone we knew in common, and often a common research interest. Also, I'm always impressed by how friendly and approachable the people at these meetings are.
• I'm so glad that I took classes on fluid mechanics and finite element analysis. I cannot imagine enjoying this meeting half as much as I did if I knew nothing about those topics.
• My talk went well. I'm glad it's done.