Galois Groups and the Etale Fundamental Group

For all those undergrads who learned the Galois theory of covering spaces and always wondered what the link was to field extensions, I wrote up a very introductory-level exposition of exploring the rather deep link, eventually leading to an algebraic geometrical discussion on etale coverings of schemes, which intersects with topological covering space theory for Riemann surfaces, and is aesthetically similar enough for intuition from Galois theory and covering space theory to sniff out possible results. The construction is thanks to Grothendieck. The theory turns out to be quite fruitful having numerous applications to number theory and the inverse Galois problem. For a much more detailed discussion, one should look at Tamas Szamuley's "Galois Group and Covering Spaces." Enjoy, and feel free to post questions.

Kaleidoscope Shattered

Ray Bradbury's death was made public today. To borrow directly from him: The shards of the kaleidoscope that had formed a thinking pattern for so long hurled away. The story, "The Kaleidoscope," is the second story in the collection, "The Illustrated Man." It is a reflection of death and demonstrates Bradbury's ability to use science fiction as it ought to be used, to liberate us from cliche and thoughts thought 1000 times over, to explore new territory.

I always took his work ethic to heart. Read and Write with hysteric obsession. It means wherever we are, we ought to both listen and create simultaneously, never tiring even until we're 92. He also said this: "I have three rules to live by: 1. Get your work done, 2. If that doesn't work, shut up and drink your gin. 3. When all else fails, run like hell. As a side note, we have the same birthday.