I'm almost halfway through my three week trip to the west, and I figured I'd take advantage of the break in my normal Cantabrigian routine to write something on live-journal.
My itinerary is as follows:
3/14-3/19: Tucson, AZ. Participating in the Arizona Winter School, a conference for number theory grad students.
3/20-3/23: Grand Canyon, AZ. Trip to the grand canyon with my parents, taking advantage of the break between the two conferences.
3/24-3/29: Los Angeles, CA. Recent Developments in Number Theory at UCLA.
3/29-4/2: Seattle, WA. Visiting my brother and sister and seeing my brother's puppy Newfoundland, Finn (who, at about 12 weeks, currently weighs 50 pounds).
4/2-4/6: Berkeley, CA. Visiting friends in Berkeley.
The winter school was fun, and moderately successful mathematically. It's organized as four lecture series on a particular topic, with a project associated with each of the lecture series. This year the topic was "Transcendence Theory," and our project was on a paper of Belolipetsky and Jones on bounding the number of automorphisms of Riemann surfaces of genus g. In particular, one can define a function N(g) which is the maximum number of automorphisms of any Riemann surface of genus g. Hurwitz showed that N(g) <= 84(g-1), and that there are infinitely many genera that achieve this bound. This result was extended in a number of ways: first by Accola and Maclachlan to N(g) >= 8(g+1), then by refining the surfaces that one considers. We say that a surface is arithmetic if it is uniformized by a subgroup of SL_2(Z) that is commensurate with the image of the elements of a quaternion algebra of norm 1 (under certain restrictions on the algebra). So you can ask for N_ar(g): the maximum size of the automorphism group of an arithmetic surface of genus g, and N_nar(g), the maximum size for a non-arithmetic surface. Then one has bounds 4(g-1) <= N_ar(g) <= 84(g-1) and 8(g+1) <= N_nar(g) <= 156/7(g-1), and all of these bounds are tight. We read a paper proving the 4(g-1) lower bound. It wasn't original, but it was fun to read and learn about, and we gave a good presentation on it (which you can find at
http://www.math.harvard.edu/~roed/AWS08.pdf for more details about all of this).
After my project group went to sleep each night, I worked on Sage until 5 or 6 or 7 in the morning with William, Craig, Robert and Robert. Robert and I are making progress on coercion, though there's still quite a bit of work to be done. I also met more number theory grad students, which is always good, and went hiking on our afternoon off. We went out the the western section of the Saguaro national park and hiked up and along a ridge. It was a fun and easy first hike of the season.
After Tucson, I headed up to Flagstaff and the grand canyon with my parents: a wonderful trip sandwiched by transportation mishaps on both sides. I took the greyhound up to Phoenix to meet them, waking up at 6:35 so that I could catch a taxi to the station and be there an hour before the bus was scheduled to leave at 8. When I got there at 7, I was told that the 8am bus was full and that I would be put on the 9am bus. FIne: I slept for a bit, then worked on adding stuff to the presentation. This dragged on past 9:00, as the bus failed to show up, and then continued to fail to show up. It finally appeared at 11:15. *sigh*
After successfully meeting my parents in Phoenix, we drove north. After a brief diversion through Sedona and Red Rock State Park (which closed just as we arrived), we made it to the bed and breakfast in Flagstaff. It was really nice: if you ever want to stay in Flagstaff, and have money to spend :-) check out the Inn at 410. We met a pair of young women from Alabama who were just returning from backpacking in the canyon. They lent us their guidebook to supplement our own, and offered us their entrance pass (which is good for 7 days). My dad decided to buy the $80 annual all-parks pass instead: the entrance pass was non-transfrerable.
The next morning, we left at 8:20, and made it to the canyon by 10. I had seen pictures, of course, but it was still awe-inspiring. After looking over the edge among the crowds for a bit, we took the shuttle bus to the South Kaibab trail. I stayed with my parents until we made it to Cedar ridge, where they were going to turn around. The weather was just about perfect. We passed a string of mules on the way down, as well as lizards, squirrels and ravens. After sticking back with them for a couple of hours, I wanted to go faster (and get further), so I continued on for another half hour to Skeleton point. The views kept getting better as one got further into the canyon and away from the crowds. If you ever go to the grand canyon, go early: the heat and crowds are far worse in the summer. I rejoined my parents at the top, and we proceeded back to the main "village" for an early dinner, then walked along the rim toward Hopi point to see the sunset. On the way we passed within a dozen feet of three bighorn sheep, who seemed completely unconcerned with us. We didn't quite make it to our desired lookout point for sunset, but I'm sure that the crowds were better where we ended up. The shadows that fill the canyon at nightfall give it a totally different look than at high noon.
We were intending to head over to a Full Moon talk by one of the rangers. We made it to Hopi Point just in time to catch the last bus for a half hour, and rode the shuttle to Mather Point where the talk was. My dad and I were unimpressed with the beginning of the ranger's speech (about how a scientist looks at the moon and sees things differently than.... blah blah blah). We decided to just stay at Mather Point and look at the moon/stars with our binoculars. The Pleides are pretty awesome through good binoculars, and we could see the Orion nebula as well. We finally decided to leave, making it back to Flagstaff around 11.
The next morning we returned, though later: making it to the canyon around 11:30. We started by going to the Kolb studio, where one of my mom's friend's father's paintings was in the permanent collection. After seeing that, we walked along the rim trail from Pima Point to Hermit's rest. It was quite nice: not many people, and all of those that we met seemed to want to help my mom learn to use her camera (including 3 professional photographers who fixed some of the settings that had been messed up, and an amateur that talked to her for about 20 minutes about lenses and how awesome a camera she had (a Nikon D300)). It was kinda funny. We were intending on heading back early, both so that I could get some laundry done and so that we could go to the Lowell observatory. But as we drove toward the exit, we saw 6 bull elk right by the side of the road, tussling with their antlers. By the time we had pulled over, taken lots of pictures and watched them for a while, we decided that it would be more fun to drive to the east entrance and watch the sunset from there anyway.
So we did. We made it to Desert View with its watchtower about half an hour before sunset. The cliffs were amazing in the setting sun: the Palisades of the Desert. We took pictures and admired the view, then continued back to Flagstaff past the smaller canyons of the Little Colorado and the roads east toward the painted desert. Overall, I was quite impressed by my trip to the grand canyon: I would like to get back sometime. Of course, I have many other national parks that I need to see as well. :-/
We made it back to Flagstaff in time to head up to Lowell Observatory, where I had done a week of astronomy a few years previously (using the astrograph to plot positions of Charon for an occultation in 2005). It was fun to see that again, and I think my parents enjoyed seeing Saturn through their 24" refractor.
The next day we managed to find a laundromat that was open on Easter, enjoyed the view from the top of oak creek canyon, went for a short hike through Red Rock State Park, and returned the rental car in Phoenix. I was in a different terminal than my parents, so I checked in then joined them for dinner. They checked through security and I headed over to terminal 2 (where the crowds were far smaller) and proceeded through security with plenty of time to take advantage of the free wireless in the Phoenix airport. At 8:10, half an hour before departure, the gate agent announced that since the plane did not have room for normal sized carry-ons (it was a regional jet), she would be coming through the boarding area putting stickers on oversized luggage so that they could be put in the cargo hold. It was at this point that I realized that I did not have my suitcase, but only my backpack. Just as I was beginning to panic, and after I had figured out that I must have left it on the shuttle between terminals, I received a phone call from someone telling me that my bag was on one of the shuttles. I thought that they said that it was being taken to the Operations Center Lost and Found, so I told the gate agent that I was leaving to try to retrieve my bag and ran off. I talked to one of the bus drivers, who took me about 50 yards to the Operations Center, which was closed. I called the woman back and discovered that there had been a misunderstanding: the bag was still on a circulating bus. She told me that the bus had left Terminal 4 just then. So I headed back and waited as the buses passed. At 8:28, just as I was about to give up, the right bus came by. I grabbed me bag, signed the form the driver held out to me, and ran. The line at security was basically nonexistent, and as I approached the gate, they were calling my name over the PA. The gate agent was glad to see me. :-) I made it on in time. Then in LA I managed to not get run over by the Flyaway Shuttle. That was good.
Thing here at UCLA are pretty good. I'm even understanding some of the talks. :-) I think the most useful thing that it's doing is focusing my attention on areas that I should learn more about. Selmer groups, L-functions, Iwasawa theory.... :-)
I'll write more about the conference when it's over, and I'm off to Seattle or Berkeley. In the mean time, I should probably sleep at some point.
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crappy