Sunday bikings and such

Although it would have been exciting to head out into the countryside this weekend, the need to clean my apartment and prepare my seminar talk ended up winning out. Saturday found me washing windows and making my fridge a place where I would consider keeping food. later in the afternoon, I decided to head in to town for some other supplies, like kitchen utensils should I ever want to make food here. I wasn't sure that there would be a place to lock my bike, so I took the TIFR bus. As is generally the case when I opt for a bus rather than a bike, I wish that I had ridden. I did manage to get a broom and some incense and some colored shawls to try to fashion into some sort of shades for my currently bare light bulbs.



In the end, I didn't find kitchen supplies. There was a woman walking with a basket full of pots and pans on her head who looked like maybe she was selling them, but I wasn't sure and I decided not to ask. I ended up walking back home because the busses don't run all that often on the weekends. I worked on my talk a little more and turned in early so that I could get up and ride in the light traffic of Sunday morning.

Which I did. I was out the door at a little after 7:00, and pedaled first down along Marine Drive (which has a new name now, but I haven't heard it used...) to Malabar Hill. As predicted, the roads are quite empty on Sunday mornings. When I first left the colony, I moved to the right of the road for a second, but quickly remembered that traffic flow is opposite here. Left turns are the easy ones, and the ones where a car coming up behind you is potentially going to swerve into you if you are going straight. I think that this switch is easier to make on a bike than in a car, partly because one doesn't have to switch sides of the vehicle as well.



Since I am so new to this place, I don't have a really good sense of who rides a bike here. There are lots of bikes out on the streets, ridden by people of all ages. Almost all of them are single speed city bikes with a diamond frame, sometimes with two top tubes. A fair number are clearly delivery vehicles, of both the huge-bundle-on-the-back-rack and the reversed-tricycle-with-a-big-cargo-area-in-front sorts. I don't think they are used to seeing non-Indians getting around on bikes; there were lots of encouraging smiles and waves people as I passed by.

I asked at tea today if there is much of a recreational cycling phenomenon in India, and those present didn't seem to think so. They were surprised to hear that people like me who don't have cars are becoming less fringey, at least in places like the Northwest.



Anyway, Marine drive is a large wide street, they were doing some construction, expanding or repaving the sidewalk promenade along the water. I stopped and took a couple of pictures - people thought it strange that I was taking a picture of my bike. This land where Marine Drive runs along was "reclaimed" from the bay early in the last century. This was once a city of seven islands, but they have been merged into one large connected mass by a series of regrade and fill projects.

From where I started at the closer end, the waterfront arcs around to the north and west past Chowpatty Beach, which was fairly deserted in the morning, but is apparently quite happening in the evenings, and at Walkeshwar starts up Malabar Hill. Coming from down in the rest of the city, this is quite clearly an upscale residential district. Even so, there were parts of it which were not sharing in the wealth displayed by the high rises of their neighbors. I rode up the hill past the sweepers and the tea sellers and the other Sunday morning people. After a few zigs and zags, I made my way down into an area near the water's edge where some people were standing about next to a stage outside of a small temple. Nothing much was going on - a few people were asleep on the stage, some were sitting about starting their day. I slowed down to look at the scene, and some children took an interest in my bike. The first thing everyone notices is the lack of a rear brake. One kid, taller than the rest and wearing a red t-shirt in particular was especially perplexed. I showed him the fixed gear, but he clearly hadn't seen one before. So I rode back up the street a little bit and demonstrated a short skid. The enthusiastic response prompted a no handed track stand, which impressed him so much that he ran and woke up his older brother who was one of the people sleeping on the stage. The older brother was clearly more interested in sleeping. My new friend asked me to wait for a minute while he ran to get his bike, which he did, and showed off riding standing on the top tube.



After this, I rode around the bottom of the hill a bit more, walked through a small park, climbed back up via a steep and somewhat windy street, past a park with lots of greenery, and then dropped down, rejoining the city by the Crosswinds bookstore. I found my way back without much difficulty, and was able to shower and change in time for breakfast at the institute, which goes late on Sundays.

Post-breakfast, I went up to my office and called Jill using the internet. She was at Davis's housewarming party, so I got to talk to Josiah, my mom, and Davis as well. It is pretty amazing how different the communications network is than just a few years ago. It certainly makes moving to the other side of the world a lot easier.

I worked on my talk some, but was generally rather lazy for most of the rest of the day. At around dusk I took a walk around the colony. The sky made its rapid shift from blue to black and the Banyan trees unleashed their birds to the evenings festivities.



This morning I called Jill to hear her story of race day number one. The first cyclocross race had none of the cold, rainy and muddy features that were expected, but was instead a warm, dry and dusty day at Steilacoom. .83 was well represented, with Jill on her lovely new bike, wearing the kit from her new team, taking 13th of 45 women (And 1st of 2 in the women's singlespeed category!), and Denny placed 7th in a field of 63! Unfortunately, Jane had a fall and hurt her rib - either a bruise or a too small to see fracture. Hopefully she'll be back up for next week.

In the afternoon I gave my talk on rationally generated arcs. The main idea is to define a potential property of a variety X involving rationally generated arcs, and show that this property is implied by unirationality (a variety is unirational if there is a dominant rational map from projective space) and it implies rational connectedness (X is rationally connected if there is a rational curve between any two points). It is conjectured but not known that unirationality and rational connectedness are different, so something that sits between them is interesting. Of course, it could be that rationally generated arcs the same as one or the other, and I haven't done anything but introduce some useless new terminology.

I got a number of questions during the talk and it took me the whole hour to get to that result, the chain of implications. In the past, I have combined this talk with a calculation using arcs to find lines, such as the 27 on the cubic surface, but I think it works well on its own. The questions were helpful for my understanding, and the talk ended up being better and more precise than what I had planned out.
In addition, the fact that I didn't go into any of the intersection theory calculations means that I can try to pick the brains of the resident experts and give a better talk on that part of my thesis sometime soon. Also, Srinivas suggested some places to try applying rationally generated arcs to poke around and look for an example.