Not much really...

Today was yet another day. It is basicly like most days are here; wake up, shower, breakfast, Riemannian Geometry, Noncommutative Geometry, lunch, power nap, read some, Noncommutative Algebraic Geometry, read some more, have supper, study and do homework, sleep etc... Because of this there isn't really that much to write about, so don't be surprised if I don't write that much while I'm here..

One interesting thing though, one of my Polish friends here and I were talking about going to swim, since there is a swimming hall on Campus, and we can go there for free through the university. Maybe tomorrow? They were open really strange hours..

Today in Noncommutative Geometry we introduced the Gelfand transform and showed that it has the same basic properties as the Fourier transform. This is nice, since I am quite familiar with the Fourier transform. :)

In NCAG (abbreviation for NonCommutative Algebraic Geometry from now on) we introduced quivers, which is really just Directed Graphs with a defined Algebra over it. For some reason, algebraists seem to like to take simple things, rename them, and then use them (I am very aware that there are purposes for this but still). Anyways, quivers will enable us to go from the Noncommutative Algebra to the Algebraic Geometry and vice versa, so that we will be able to use methods directly between them. The name quivers is quite ingenious though, because a quiver is the container that holds the arrows for an archer, and directed graphs basicly look like arrows, so a quiver becomes in the same sense the thing that holds the arrows.

I found out something interesting as well between classes, when I spoke briefly to our professor, Massoud Khalkhali. I asked him if we were going to cover the Non-Hausdorff spaces in the course, and his response was that we weren't. All that we will cover is the spaces that can fail to some extent to be Hausdorff (wikipedia it you are wondering what a Hausdorff space is). That is an interesting case, but I don't think that is where we will find the answers that explain the universe. I think that the Geometry and Algebras that will explain most of Physics and Mathematics are actually contained in the abstract spaces which are not Hausdorff at all. But as it seems, there isn't much progress in that field, because well it doesn't really make sense..