Lots to talk about here, so I'll actually include section headings.
More Good Food
Sometime around last weekend, I was in my office on the computer, and a westerner knocked on the door and asked in English where to find Ms. Yu. I told him to look in room 1307. As he thanked me, Pin popped his head out from behind the door, saw who was standing there, and said "Bonjour". The person was a bit surprised, and proceeded to try to converse with Pin in French, which Pin declined by answering in English. Turns out the stranger is Professeur Claude Viterbo from École Polytechnique.
In any case, Saturday, for lunch, partly to welcome Prof. Viterbo and partly to say farewell to Profs. Bismut and Ionescu (plus the fact now altogether we have a party of 7, with Ms. Yu included), we had lunch again at Qiao Jiang Nan (South Beauty; this time I checked the correct English name given on their card). We made good use of the "50% off" menu that Ms. Yu acquired last time, and so the meal came out to be around 260 RMB, a pretty decent price for the kind of food we got. Yum.
Pin and I tried to be sneaky and pay the bill ourselves, unfortunately our professors were too quick on the uptake, and so the four of them split the bill instead of the two of us. Ah... the difference between Chinese and Western customs.
Shopping Expedition
So I finally went to Wang Fu Jing (Well at King's Court? I am not quite sure how to properly translate it).
Alex (Ionescu) wanted to by some souvenirs for his wife and daughter before leaving for Wisconsin. Ms. Yu was busy, so Pin and I went on an small detour taking Alex shopping. Alex wants some kids' toys and some wall scrolls (painting/calligraphy)--something characteristically Chinese. That was why Wang Fu Jing was suggested.
To get to Wang Fu Jing from Peking University isn't the easiest thing, the problem being that the Olympics is coming the China in about a year (the tickets just went on sale Sunday, on the first day of sales, 50 thousand orders were placed for over 250 thousand seats). The Chinese government pledged to complete its subway project by the end of this year. (This is a project that has been going on for the better part of a decade and so far has only two completed lines out of the projected 6 to 8.) Once the subway is completed, public transportation in Beijing would be much more convenient: currently there is a east-west line that runs through the heart of Beijing, and a second loop-line that runs around the second ring of Beijing (Beijing is divided into Huan [rings], centered around the forbidden city. The first and second rings represent much of the ancient Beijing, and the third and fourth rings are also well developed. Up to the 6th ring can already be seen on the maps.). Once the subway completely finishes, there would be a line that goes all the way out to Peking University and Tsinghua University, that goes all the way in the other direction to the airport (which would make it very convenient for visiting scholars). The big traffic jams outside my office day-in-day-out is due to primarily this: the subway construction is at about one intersection away from reaching Peking University.
This convenience in the future brings much inconvenience now, unfortunately, since the construction makes both taxis and busses slow around this area. In fact, the construction means that the most direct route from Peking University to the city center is often stuck immobile. So what we did (good that Pin came here for college) was to first take a cab to the West Gate subway stop on the loop line (roughly 10 km from the university) and transfer from the loop line to the east-west line, from which we get to Wang Fu Jing.
The subway was full of people. It is much more crowded then even the most crowded NY subway car I've been on, and also much more crowded than the typical Taipei Metro. The cars themselves are rather nice: clean and rather quiet (though that might just be the crowd drowning on the mechanical noise). I am slightly surprised at the fact that they still allow the use of paper tickets which gets collected at the gate by real people (they also simultaneously allow the use of RFID IC cards for bus rides, as well as paper tickets sold on board the bus, so on each bus there would be at least 2, sometimes three company employees: one driver and one or more conductors [I've read about these conductors {Che1 Zhang3}, apparently they were also the norm not 20 years ago in Taiwan]; the IC cards are also good for use at the subway) I guess this goes back to the cheapness of labor again: when human employees are cheaper to maintain than machines, who would want to install high-tech equipments?
There is a huge shopping/pedestrian area around Wang Fu Jing, it is obvious that the are has been specifically developed for tourism. When I first got to Peking University, I was surprised at the number of Caucasian faces I saw; when I got to Wang Fu Jing, I felt more like in Chinatown, New York than in China! On the roads and in the shopping centers were seas of foreigners: not just Caucasians, but also Japanese and Korean Tourists, American businessmen, some Arabs: much more than I am used to in an Asian city. (I don't think Taipei was ever, nor will ever be, so international.) The sales clerks saw Alex's 6-foot-3 build and curly Caucasian hair, and they just crowd up to us trying to sell us souvenirs in their broken English. Pin cautioned us against buying anything without haggling.
To my amateur eyes, Pin is a god at haggling, yet according to him, his skills are nothing compared to any typical Chinese woman, his wife included.
We first went into a silk shop: the prices are okay (compared to, say, prices on silk in Hong Kong which I know from experience), but we didn't catch anything spectacular (also I am running low on space in my suitcase, so I try not to buy large items; though I was really tempted to buy a ZhongShanZhuang (the kind of clothes that Dr. Sun Yetsen wore, as a Chinese "equivalent" to the western three-piece-suit). Then we went to a department store, which on the outside claims to be a store for toys and children's clothes, though in reality contains much more than just that.
In terms of toys, Alex looked for stuff he couldn't find overseas. One particular item was a 3-d wooden puzzle: you pop the shapes out of a particle board (the shapes are pre-cut on the board) and assemble them together. I had quite a few when I was a tiny kid: I remember buying dinosaur ones at the Taichung Museum of Science and piecing them together with my dad. I also remember bring my T-Rex one with me to Kindergarten show-and-tell and breaking it during the recess afterwards because I wouldn't put it away (I was afraid someone else might break it; ironic that I then fell on it myself and broke the model). In anycase, Alex bought one of Tian Tan (Heavenly Temple) that looks really difficult and another one of a dragon-boat. (Pin pointed out that part of the department store was state-ran and thus one shouldn't try to bargain there.) Alex also bought some Chinese clothes for his daughter.
Then we went upstairs.
That's when the sales people really started latching on to us. (Pin pointed out that usually, this means that those stores/stalls are privately owned/leased, so one can and one should bargain with them.) The first thing we saw were some fans: nice Chinese folding-fans that either have silk-face with prints of Chinese paintings, or ones that are made of carved Tan-Mu (a kind of fragrant wood). Pin got a deal of three fans and one wooden fan stand for 80 RMB. (They were asking for 160 RMB for one fan to boot; the process was also kind of funny: Alex wanted to buy a fan stand, so Pin asked for the price: the saleswoman attending to us gave a price of 20 RMB, so Pin immediately blew her off and made a counteroffer of 5 RMB. When they are haggling (the saleswoman insisting that she cannot sell it for such a low price), another saleswoman came by, listened to the conversation for a while (during which, curiously, neither Pin nor the original sales mentioned the original offer), and interjected with an offer of 25 RMB... well, Pin immediately called bullshit on that "She here offered me 20 to start with, and now you want 25?" and that sort of gave Pin additional ammunition for the final deal.)
And then we went to buy wall scrolls. Pin got even more brutal here. He claimed (I'm not quite sure whether it is true or not) that his father did calligraphy for a living. So he was making all sorts of criticisms on the scrolls (the ink is too thick here, the hand is waverly there, the presentation is not clean, the picture is too crowded, too many colours, too many lines...). There are some flaws I could see on some of the paintings, especially on those with bamboos (somewhere along the line I picked up how to judge Chinese bamboo paintings based on calligraphic principles), but nowhere near that many. One of his best techniques, I think, is that he always asked the seller to give him a "honest price", and no matter what the seller says, he just shakes his head and laughs. From a purely information-theoretic manner, that is a wonderful way to bargain for a good price: as long as you don't reveal your bottom line, the sellers doesn't have any way of "seeking a middle ground", and good use of this technique should win a better price.
One curious shop I saw in Wang Fu Jing is a Kuai Zi Dian (Chopstick Shop). And indeed, the entire store only sells chopsticks (well, also chopstick holders and a few bowls and plates). I think that was rather neat. I almost bought a pair of silver chopsticks with carrying case, the chopsticks dissemble the same way pool-cues do, and the four pieces gets packed compactly into a nice tube that's roughly half the size of a toothbrush carrying case. I think the idea was neat, especially the prospect of bring my eating utensils with me. But then I realize that I would then want to wash my chopsticks after I eat, and for which I will need to bring detergent etc. So all things considered it might be a bit of a hassle.
Mistake! Ahhhh!
So it turns out that my simplifications of my senior thesis contained a major flaw. I didn't realize it was such until I tried to present it to Pin and Sergiu and Pin pointed out the mistake. I tried to put too strong a condition on the solution to a given set of equations, and only a vacuous solution could satisfy the condition (well, a priori anyway). I've been working on fixing the problem for two days now, and I have an idea, which, curiously, imposes an even stronger condition on the solution (though I realized that I could do so by exploiting some special orthogonality properties to restrict the solution space). I'll work more on fleshing out the idea tomorrow after Pin and I give our lecture on bilinear estimates.
A three line, flawed argument in the original paper will now have to be replaced by a 3 page minimum argument. I'll have to check over it several times to make sure it is water tight. Hopefully I can push this modification forward with not problem so all my other work on the later part of the problem isn't moot.
(To be more precise, I tried to solve a divergence equation for a vector field with Dirichlet boundary conditions, which, well, isn't really appropriate. Classical studies of boundary value Hodge systems [c.f. Günter Schwarz's "Hodge Decomposition", LNM 1607] suggest that the proper boundary condition to impose for divergence equations should be a Neumann condition [and a tangential Dirichlet condition usually goes with the curl equation] [by divergence and curl, of course, I mean the co-differential and exterior-derivative]. My plan now is to solve the problem without imposing exact boundary conditions, but to follow Corvino's convention and impose decay condition near the boundary. According to Corvino's paper I should be able to impose such conditions so long as the dual operator has trivial kernel, though I do have to check a few other compactness conditions and check that the variational formulation still makes sense at this level, since I impose additional conditions on the dual space that makes it more like a moduli space of the standard L2 space.)
Update 04/25: Ian Lai pointed out to me that tan2 mu4 is actually sandalwood. Thanks.