Blog: Articles filed under travel

It is Saturday, but it doesn’t feel like Saturday, mostly because I’m … at school. This is the last day of the CUMC. I’m in the last talk of the day, having chosen to attend “Perfect Matchings and Shuffling.” Afterward, there is the final keynote, which Ram Murty will deliver on the Riemann hypothesis.

Yesterday I went to a talk on fractal image compression. The talk itself was not stellar, but there were some good questions on the applications of this type of lossy compression, and the speaker addressed those well.

In the afternoon Aaron, Rachael, and I took a bus—yes, a bus—down to King St. This was my first time riding public transit, and it wasn’t in my own city! Aaron wanted to visit a small record store, Orange Monkey Records, and then i checked out a used bookstore known as Old Goat Books. I bought more books than I should have, considering they need to fit in my sparse luggage—but I couldn’t resist.

The final keynote of the day was delivered by Greg Brill, of Infusion. Although titled “The Evolution of Technology,” Brill’s talk was not what I expected. He has a Masters in computer science (after coming from a liberal arts background!) but talks like a showman rather than an academic or a businessman. He discussed how mathematics—and hence, mathematicians—are essential to the development of technology, particular business products. For example, he mentioned how his company had been working with motion-sensing technology similar to Kinect, and that the main problem was not a lack of technology but a lack of the mathematics necessary to achieve what we want in that area. Brill is very keen on the idea that we are moving from an idiomatic society to an idiom-less one and is convinced that mathematicians will help make that happen.

Dinner came in banquet form, and while the food was OK, the dancing was better. That’s right: dancing. I love to dance, and I had a great deal of fun on the dance floor for about an hour or so before calling it a night. I’m not as young as I used to be.

Tonight we fly home, and tomorrow I go to my nephew’s first birthday party (no weekend recovery for me). Then it is back to math research: reading papers, re-reading papers, writing algorithms, and making tea. CUMC has been fun, but I will be glad to be home.

It is Thursday, July 8.

After the first talk this morning—on set theory, particularly ZFC—I spent time caressing the lovely wireless network by way of uploading some photos to Flickr. When attempting to geotag them, however, I ran into the slight problem, in that typing “University of Waterloo” into the Flickr map’s location finder produced no results.

So, Yahoo!, in case you are wondering why people drool over Google and its products, here is a hint: we are lazy. When I type in the name of a major university, your map should be able to find it for me. I should not have to go find a postal code on my own, enter that, and wind up in the general vicinity of the campus. (I used Google Maps to find the postal code too, which just seems wrong). It is not that I am a Google fanboy, Yahoo!—they just do it so much better.

At lunch, I did something completely out of character and chose to be adventurous, purchasing bubble tea for the first time. My less adventurous self was soon vindicated. We went to a fast food place called “The Grill” for food. I attempted to poke my straw through the seal placed over my cup—urged on by Rachael’s encouragements of, “Just do it!”—and after one mighty stab, the straw went through … and the bubble tea exploded. A plume escaped from the top, but the cup also developed a leak in the bottom somehow, and it spilt all over the table and down onto the floor. We don’t cry over spilt milk, but what about spilt bubble tea?

I also decided to be adventurous when it came to food. The menu had a “lamb burger” on it. I have had lamb before, but never in burger form, so I ordered one of those. Its taste was similar to a regular hamburger, which disappointed me.

For some reason, I was lethargic after lunch and greatly desired a nap. I blame the heat. I struggled to stay awake and pay attention to the afternoon’s talks—first one on computability theory, and then another on universal algebra. After that, we had a little break before going for dinner. Rachael and I ordered some chicken fried rice from a Chinese place, while Aaron opted for shrimp wonton soup. The price was right and the portions huge—I could not finish mine, although I came close, while Rachael ate a lot and left even more.

The morning keynote speaker was Michele Mosca, from the University of Waterloo. He talked to us about quantum computing, with a particular focus on quantum cryptography. The talk was more about mathematics than of mathematics, with only a little actual math involved. I quite enjoyed the subject. Quantum computing is a concept that sounds like science fiction, but it is real; we have quantum computers—albeit primitive ones—right now! The future is here.

It is Wednesday, July 7. The CUMC talks began today.

I went to four talks today. Rather than summarize them all—I enjoyed them all—I’ll mention some highlights. The first talk of the afternoon was both my least favourite and most favourite talk. Entitled “The Ontology of Mathematics: Do Numbers Exist?,” the presenter read from dense slides, which did not make for the most riveting experience. There was some lively discussion among the audience, however, and I enjoy talks like that.

Comparing CUMC to the Combinatorics & Optimization workshop that preceded it, I prefer the student talks of the former. The topics are so varied—there is so much choice within each time slot, that it is difficult to decide which talks to attend. The atmosphere is less intimidating, because it’s undergraduates talking to undergraduates. I almost regret not giving a talk myself—almost, for it would involve public speaking, and long gone are the days when classes made that mandatory.

There were two keynote speakers, one at lunch and one at the end of the day. First, Frank Morgan, from Williams College, gave a talk on densities and the Poincaré conjecture. As I have never studied differential geometry, most of the mathematics went over my head. The audience in general got into it, however, asked great questions, and we all tried answering the questions Morgan asked of us. In the end, I learned from the talk, which is all one can ask, right? The second talk was easier for me to understand, because it involved matrices and metric spaces. I love metric spaces! Carsten Thomassen, visiting from the Technical University of Denmark, was the speaker; he also gave two talks at the Combinatorics & Optimization workshop.

After the last keynote, Aaron, Rachael, and I walked down to the campus plaza, which has a cornucopia of restaurants. We elected to share a pizza, placed an order, and then took it back to the air-conditioned environment of another building. The Waterloo campus is beautiful, but the heat makes any sort of lengthy walk unattractive. Waterloo campus is also big—compared to Lakehead’s, at least—so every walk is lengthy.

The pizza proved a good choice, as it was tasty and filling. We walked back to the residence where Aaron and Rachael stayed, and then Rachael and I listened to Aaron’s talk, which he is presenting tomorrow afternoon (it concerns the classical Cantor set). Tomorrow I plan to attend talks on set theory, computability theory, universal algebra, and perhaps one on range-sum queries.

I’ve uploaded some photos from my trip so far. They are all accessible in this Flickr set, and new ones will be added there as well.

It is Tuesday, July 6.

Today’s four talks began with electrical networks and random walks. That is, suppose you have a graph that describes a network through which electricity flows. Starting at a vertex x, what is the probability that, when walking at random along the graph, we will arrive at a vertex s instead of a vertex t? This talk was very easy to follow (for which I am thankful), even though I don’t have any engineering or physics background with which to understand the electrical current aspects (like voltage law).

Unfortunately, the second talk involved probability. Probability is great, but I find it very difficult, so this talk was hard to follow. The third talk was about embedding locally-compact metric spaces on surfaces (it is not as scary as it sounds). Finally, the fourth talk was about matching polynomials. The speaker went rather briskly, so it was difficult to take detailed notes, but I enjoyed the subject. Before this summer, I had no idea that polynomials and graphs went so well together. Now it seems like they’re inseparable.

And that concludes the Combinatorial and Optimization workshop. There was a banquet for CUMC at the Huether Hotel, and it was not what I was expecting—very crowded, although the food was good.

Prior to the banquet, Phelim P. Boyle delivered the first keynote speech for CUMC. Boyle is a mathematician of finance, he is interested in the recent financial crisis. He discussed option pricing and the Black-Scholes equation. As with probability, finance is an area of mathematics I avoid, because of its strong dependency on number. Nevertheless, I enjoyed the talk.

I now have access to reliable wireless on campus, although such a phenomenon continues to elude me at my grandparents’ house. Never has my dependency on the Internet been so apparent.

I wrote this last night at my grandparents’ house, which has no Internet connection I can feasibly use (dial-up does not count), so I had to wait until today to post it from the University of Waterloo campus. All references to “today” refer to Monday, July 5.

This week, Rachael, Aaron, and I have travelled to Waterloo, Ontario for two math conferences. The first is the Combinatorics & Optimization Summer School, a two-day event consisting of several talks and, yes, food! The second is the Canadian Undergraduate Math Conference, which also entails much talking and eating. I was reluctant to attend at first, because I dislike travelling. However, my grandparents live in Waterloo, so this was a convenient way to visit them for a week while still getting paid. With that incentive, I managed to convince myself that these conferences would be interesting and probably even useful to my research. This was only the first day, but so far I remain convinced in those respects.

I’ve been up since 4:30 in the morning. Let me take a moment to reflect on the fact that we flew from Thunder Bay to Toronto in an hour and a half, traversing—or rather, bypassing—the largest freshwater lake in the world. And we did it in a metal behemoth that harnesses complex physics and engineering to work miracles.

Flight is awesome.

OK, science-geeky moment over: back to math.

Today there were four talks. We arrived late to the first talk, by about fifteen minutes, but it was still very interesting. It concerned the colouring of graphs on surfaces.

Following a short break, the second talk discussed the Borsuk conjecture, which asks a question about the existence of a certain partition of any set in d dimensions. This was my favourite talk of the day, for several reasons. Firstly, I learned a lot about the diameter of sets, a topic with which I was not familiar. Topology involves a lot of geometry, something for which I lack proper intuition. Yet still it interests me, probably because of its ability to formalize that geometry. I like abstraction. Secondly, the presenter told the story of how Kahn and Kalai proved the Borsuk conjecture false. They took a problem that had been open for nearly seventy years, solved it in a week, and wrote a short, about one-paragraph proof. It’s a wonderful example of how unpredictable and exciting mathematics can be: sure, sometimes math research involves long, boring days reading papers and staring at a problem on a chalkboard. Sometimes, just sometimes, it leads to the most interesting results.

After lunch, we listened to a talk about cutting cake—specifically, how to divide a cake into sections such that no one person would complain that he or she received a worse section. It was by the far the most accessible of the three talks, and the presenter had a very engaging manner. Unfortunately, my fatigue caught up with me during this talk, and I found myself nodding off during the most interesting parts. We learned a little about hypergraphs, which, as the name implies, are like regular graphs but on crack.

The last talk was on symmetric groups and their combinatoric properties. Last week, my prof showed me how we may be able to make use of the symmetric groups to solve the problem on which I‘m working this summer. The talk was more of a review of things I had already learned in group theory two years ago, which was still useful considering the gap in time.

The day began winding down as we went to a pub-like house for dinner. Then we trekked across campus to the residence where Rachael and Aaron are staying. We got lost in the process, of course, but eventually found our way thanks to a map and, moreso, a helpful student.

More to come on Tuesday’s schenanigans tonight or tomorrow morning!

I got up slightly before 7 AM today, which is a feat unto itself. Bathed, ate, went online for a little. We left before 10, gassed up at the prohibitively expensive gas station, and were on our way.

I took the time to work on Jonathan Strange & Mr. Norrell, which is a very good book. Crossing the border wasn’t difficult, although there was a long lineup. Then we were in the US of A, travelling along Minnesota highways. A land where metric is only a word and everything else looks the same as Canada… .

It was the last day of the Fishermen’s Festival, so everyone in Grand Marais was out to see a parade going on later that afternoon. When we arrived, my brother and I skipped rocks for a while before my entire family went window shopping. We navigated our way down to the Angry Trout Cafe, a restaurant where we always have lunch because of their tasty fresh fish.

I had fish and chips (Lake Superior Herring). My brother had the same, only with Alaskan Cod as the fish. My mother had something … and my dad had Malaysian peanut soup, although they mixed up his order and brought him chowder at first. The food was, needless to say, impeccable.

After that, we skipped rocks a bit more to finish off lunch, then went shopping for souvenirs. I got a stuffed moose, my brother a remote controlled car and binoculars of some sort. My mom purchased a sweater.

We were on the road again after some ice cream (in a real waffle cone!) and soon enough crossed the border (paying some GST, apparently… .). We were home pretty quickly, and then I did stuff before writing this.