Well, I keep putting off writing a new post because I’m not sure what I’m going to do it on. I had an idea. I work with Calabi-Yau varieties a lot, and so inevitably the term “mirror symmetry” appears all over the place. I’m mostly interested in arithmetic properties of Calabi-Yau’s where mirror symmetry doesn’t apply, so I know absolutely nothing about it. Since I’m curious what is meant when people use this term I thought I’d do a series of posts trying to explain the main idea of mirror symmetry.
In fact, a week or so ago Matt Ballard (who graduated the year I started grad school at the same school) put up on the archive a really nice introduction to the subject. This means I even have a nice reference to work with now. Here’s the problem. To type up something fairly reasonable on the subject is going to be a major undertaking. I have very little old blog material that is relevant, so I’ll basically be starting from scratch. It is also going to be quite time consuming since I know nothing about it.
This is my dilemma. I’d love to learn about it and blog about it, but I’m not sure it is worth the time and effort it will take. I’m at that point of grad school where I probably shouldn’t go off on a wild tangent for a long time just because I want to know what this term means when it has basically nothing to do with my research. On the other hand, one of the purposes of this blog is to keep me doing things that aren’t directly related to my research so that I maintain some sort of breadth.
I’m just throwing the idea out there for you all. What do you think? Do you have an interest in hearing about (homological) mirror symmetry, because if there seems to be interest, then it is probably worth doing.