More random updates

I’ve been reading a lot of mathematics lately, but I don’t feel capable of explaining most of what I’ve been reading about, so I’m not sure what to blog about these days. Fortunately, SPUR will be starting soon, so I’ll start focusing on relevant material for my project eventually. Until then, here are some more random updates.

• Martin Gardner and Walter Rudin both recently passed away. They will be sorely missed by the mathematical community, although I can’t say I’m particularly qualified to eulogize about either.
• For my number theory seminar with Scott Carnahan I wrote a paper describing an important corollary of the Eichler-Shimura relation in the theory of modular forms. The actual relation is somewhat difficult to state, but the important corollary relates the number of points on certain elliptic curves over finite fields to the Fourier coefficients of certain modular forms of weight . You can find the paper here. Although the class is over, corrections and comments are of course welcome. (Though I hope Scott doesn’t change my grade if someone spots a mistake he missed!)
• If you’re at all interested in the kind of mathematics where planar diagrams are used instead of traditional algebraic notation for computation, you should read Joachim Kock’s excellent book Frobenius Algebras and 2D Topological Quantum Field Theories. The book is much less intimidating than its title might suggest, and it is full of enlightening pictures and discussions. You might also be interested in a related MO question.

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Random updates

I won’t have time for a substantive update for about a week, so here are some bullet points.

• Peter Cameron has a blog, which I somehow didn’t know before. Terence Tao and Tim Gowers both have links to it, but the Secret Blogging Seminar doesn’t. Anyway, it’s excellent.
• I’ve been looking over the course listings at Cambridge for Part II. Conclusion: by Cambridge standards, I ought to know more physics.
• Andrea Ferretti recently started a new math website, MathOnline. It’s for posting links to free mathematics resources on the internet. I think all of my favorite online resources are already on it, so I haven’t contributed anything yet, but I’m happy that they’re all gathered in one place.
• I’ve also been reading Kassel’s Quantum Groups and Turaev’s Quantum Invariants of Knots and 3-Manifolds, in part to better understand Scott Morrison’s answer to my question about the Catalan numbers, but mostly because what little I know about the subject is fascinating. But I feel guilty about doing this; I can’t help but feel that as an undergraduate I should be paying more attention to my fundamentals and learning about fancy stuff later. What do you think?

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