Whee! Two wonderful dinners in a row.

Wednesday afternoon, Ionescu was invited to give a seminar on some recent stuff he has been studying with Sergiu. The problem is that of unique continuation: in particular, they want to say (roughly) that if there is a space time metric with a timelike killing vector-field (so a stationary solution), such that it agrees with the Kerr metric on the event horizon, then outside the horizon it must be Kerr. The initial model problem they use is the unique continuation problem for the wave equation in Minkowski space across the null characteristc cone. They do so by proving a Carleman estimate. In a sense, that part of the proof is a concrete version of Hörmander's abstract unique-continuation theorem for solutions to linear equations (by studying pseudoconvexity of the relevant domain and the principal part of the linear operator).

In the evening, the seminar organizers invited the speaker (Ionescu) to dinner at the "faculty club". Sergiu was also invited, along with his family. All this were arranged before hand. Now, after the seminar, Pin and I stayed to discuss a few things about the talk with Ionescu and Sergiu. The seminar organizer walked in, saw us, and inquired whether we were Sergiu's students. And there, spontaneously, we got invited to dinner also.

We ate at the third floor of Nong Yuan (Farm house?). Nong Yuan has three floors. The first floor is sort-of buffet style: you grab whatever you want and check out at the cashier, somewhat like the food court in Frist Campus Center (but much bigger). Pin thinks the food there isn't good, so we usually go to the second floor. The second floor is the style I described before, where there are many stalls and you pay with the dining card as you order the food.

The third floor (this was my first time up there; and Pin's second time) is an actual restaurant, with a Maitre d' and waitresses and so on. The food there is rather better than the things we usually eat at the dining halls.

Since Alex (Ionescu) is leaving this weekend, last night Sergiu threw a goodbye party for him. We went out to dinner at a restaurant on the third floor of our office building, called Qiao4 Jiang1 Nan2 (the official translation is Southern Beauty). The food was even better than the food on Wednesday (of course, the price tag was also rather impressive: with that kind of money in China, I can keep myself fed for at least three weeks). (And we didn't even order any of the outrageously expensive dishes: there was one fish dish there that costs the entirety of our dinner bill and some, of course, that makes about 40 dollars US, so not that much more than a good restaurant in the US, but still.) Pin and Ms. Yu took care of much of the ordering, and they treated our western guests to their first Do Hua (Tofu flower). (There is also a wonderful soup made with fish, bamboo shoots, mushroom, and Chinese pickled mustard green; the best part about it is that it was served in a HUGE bowl.)

Had to give two lectures yesterday. First I TAd for Sergiu's class. I finished talking about Strichartz estimates (continued from Monday). Monday's class was not that great: I tried to give the class in Chinese, and I realized that I couldn't even get through half the material I planned. The problem is two fold: one, I am not familiar with much of the analysis jargon in Chinese, so if I want to give a math class in Chinese, I have to pause every now and then and try to remember how Pin would have said the same thing; two, I have my notes written in English (a habit I do not plan to change, especially since my English handwriting is more legible), and trying to sight-translate turned out to be a lot harder than I thought it would. So I end up having to stop and start and stop and start, which is very annoying to both me and my students.

For yesterday, then, I gave my class in English, and things went much smoother (for me, anyway, who knows how much the students got out of it; I had a lot of material to get through and only about 1.5 hrs). I managed to review quickly the proof for the non-endpoint case (using of course the abstract formalism of Keel and Tao) and finish the proof for the endpoint case, briefly sketch the proof for the retarded estimate, and "prove" that the Stein-Tomas operator, the Schrödinger operator, and the Wave operator all can be written as evolutionary operators satisfying the dispersive conditions. (For the wave operator, I did a bit more, and showed the proof for the actual Strichartz inequality for d'Alembertian; so I did the Littlewood-Paley decomposition and showed how to re-sum them in the end, and also explain why for the L^∞ case one needs Besov spaces.

The second talk yesterday was for our small seminar with Alex and Pin and Sergiu. I tried to give an overview of the foundamentals of spinor formalism for General Relativity. It went okay, but we got distracted into other possible applications of spinors rather quickly, and Sergiu got into a discussion with Alex that I barely followed.