Combinatorics and Optimization, Day 2

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.