I decided to finish my accounts of Day One comic-book style. After all, this is the city of laissez faire, so I will let myself do as I do.
The first talk I attended at the meetings was Denis Auroux’s, entitled The symplectic geometry of symmetric products and invariants of 3-manifolds with boundary, in the Sheraton Ballroom at 10a.m. Auroux started by apologizing for how technical-sounding his title was, and said that it was in fact a very accessible talk. He said he preferred this to talks with simple-sounding titles that turn out to be very technical. As someone who got lost quite quickly (Heegard-Floer TQFT -Topological Quantum Field Theory – was mentioned in the first five minutes) I think the title was just right… (To the left, Denis Auroux answers some questions from an audience member.)
After this I had lunch at the Cafe Fleur de Lis, had a decent spinach salad, but my lunch buddy ordered the BLT which turned out to be a triple decker with a ton of bacon in it. Let’s just say it’s not for the faint of heart.
From 1-2pm I attended Lubotzky’s first colloquium lecture, which was so good it got its own blog entry. Search January 6 posts for more on that.
Immediately after I attended Yuval Peres’s intriguing talk Laplacian growth and the mystery of the abelian sandpile: A visual tour. Peres explained a few computer simulations that were very closely related and which exhibited interesting common patterns. They all have the same initial setup: a lattice on the plane, and a particle at the origin. In Diaconis-Fulton addition, one adds another particle at the origin, and this particle takes a random walk on the lattice until it finds an unoccupied spot. If this experiment is repeated many many times on a computer, the limiting shape seems to be a disk. Interestingly enough, in a slightly different example, the so-called Rotor-Router model, each spot on the lattice has a direction, and the particle moves according to the direction the “origin” is pointing in. This arrow rotates clockwise (or counterclockwise? I forget) every time the particle moves. The particle again stops moving when it encounters an open spot, and the limiting shape is still a disk. The third model is the sandpile model. In this case, the lattice points all have mass 1, and when we add mass at any point, the site divides the excess equally among its four neighbors. If one starts with only mass 1 at the origin and adding mass 1 repeatedly, the limiting shape also seems to be a circle, with mass 1 in the interior, fractional mass on its boundary, and zero mass on the exterior. The big result is that one can use known results in free boundary problems in PDEs to understand and prove these patterns, namely that regardless of the model the limiting region is a disk. Multiple starting points are more complicated, but seem to still be bounded by algebraic curves. Finally, Peres presented the “mysterious” abelian sandpile problem. I found it interesting that it seems like the simulations are ahead of the math. In my experience, simulations are used to understand the math, so it is nice to see these roles reversed.
I then went to a couple of receptions. The first was a reception for FOCUS magazine affiliates (I just became a member of the editorial board), and to honor outgoing editor Fernando Gouvea for his many years working for the magazine. This was a fun event and a great way to meet other math-writing enthusiasts.
The next reception was organized by Project NExT (I was a Project NExT Fellow last year) and the Educational Advancement Foundation. The EAF is focused on promoting and supporting Inquiry Based Learning, and was founded by Harry Lucas (pictured on the left). Lucas took a mathematics course taught by R.L.Moore in the University of Texas at Austin, and from then on he was hooked on Inquiry Based Learning and helping other people learn about this style of teaching. I myself have taught a few courses this way, and have found it a very rewarding (albeit challenging!) experience. It was great to see a lot of the people who have mentored me on these teaching issues, as well as other Project NExTers.
Dinner was at a Bennachin Restaurant in the French Quarter, which was quite good (they serve African food).
Afterwards, I worked for a while at the Marriott Lobby with a friend. It was quite funny to see so many mathematicians gathered at the bar working, talking, and checking email. I don’t think I’ll ever get used to how many of us there are everywhere. On the left, you can get an idea of what it was like.
As expected, I didn’t go to everything I wanted to go to and I didn’t get to write as much as I had hoped, but I ran into a ton of people and I had a blast.