Eigenmumbles

I’m writing this from the airport in Philadelphia, where I am half through my return trip from the SIAM Annual Meeting in San Diego. I ran into a lot of familiar faces, including many I haven’t seen for a while – the last big annual meeting that I attended was the International Congress on Industrial and Applied Math (ICIAM) meeting in Vancouver in 2011, though I’ve attended many smaller meetings in the interim.

Though I came primarily to talk to some people, I enjoyed several of the talks. Nick Trefethen and Stan Osher both gave entertaining plenary talks, which included both topics one might expect, like Chebyshev polynomials and hyperbolic PDEs, and some that were a bit more quirky. Trefethen used a version of the “Snakes” computer game to illustrate the Lebesgue constants for Chebyshev and uniform interpolation, while I’m pretty sure that the video Osher used in one of his examples was someone dancing Gangnam style. In terms of presentation pizzaz, though, it would be hard to beat this year’s Block community lecture by Anette Hoisoi of MIT, which was (mostly) on biologically-inspired design. I’m entertained by just the idea of a robotic clam digging in the sand or a robotic snail crawling in a trail of slime, but it’s hard to do justice to how excellent the presentation was without the pictures. Fortunately, the past few Block lectures were videotaped, and are now available online, and I expect this year’s lecture will not be an exception.

At a more technical level, I really enjoyed both plenary talks on Thursday afternoon: George Sugihara’s lecture on correlation and causality in nonlinear systems was intriguing and beautifully explained, and Lexing Ying’s lecture on interpolative decomposition was a nice introduction to some of the key ideas underlying rapid advances in fast direct (or near-direct) solvers for PDEs and integral equations developed over the past few years. I also particularly enjoyed the minisymposia on advances in eigenvalue solvers (naturally) and algorithms for manycore machines.

Of course, I missed a lot of talks I’m sure I would have also enjoyed. The annual meeting is big enough that there are many, many parallel sessions, and inevitably a few of the ones I find most interesting are going to be in direct competition. I missed a structured solvers minisymposium that I’m sure I would have enjoyed in order to go to the eigenvalue solver talks. I also missed the Chebfun minisymposium on Wednesday afternoon in order to attend the linear algebra contributed presentations. This made me particularly sad, because while Trefethen’s plenary talk was entertaining, it was stuff I’ve seen before, and all very high-level stuff at that. There’s some nice approximation theory underlying Chebfun, modern computational takes on classic topics from complex analysis, Fourier analysis, the theory of orthogonal polynomials, etc, and I would have enjoyed seeing some talks with more details of those contributions. But I’d already agreed to chair the other session, and I was giving the first talk (on a recent paper on Localization Theorems for Nonlinear Eigenvalues with Amanda Hood) – and so it goes.

After four days of talks and socialization (and a red-eye flight), I’m worn out, but happily so. Time to go home, now, and I’m looking forward to a quiet week in Ithaca before I head off to the next meeting.