456 words on UniThe New York Times had a picture series about people doing mathematics (odd footwear inclusive). Hopefully that'll stop people wondering why we'll hate anyone who wants to take away our blackboards.
Today we have a departmental summer party and our electronic blackboard which can communicate with another board over the net has been demoed. I nice toy! Particularly if the people you want to discuss things with were further away than just down the corridor.
Before, we heard a talk in our colloquium about encryption using elliptic curves. Nothing new to me, mathematically, as I once organised a series of talks on cryptography at Warwick and taken a course on elliptic curves there as well. But the guy who talked works for an electronics company by now, which meant (a) that the guy used computer presented slides rather than a blackboard (b) that those slides had his employer's name on every page (c) but not his own and (d) that he focused on some practical issues of implementing elliptic curve encryption in the limited environment of smart cards. The last point was a non-mathematical yet interesting aspect. [To his merit I must add that he was still enough of a mathematician to use the blackboard for further additions. He seemed to enjoy talking to a real mathematical audience again, noting that
people may actually understand what I'm talking about.]
Heard another talk about topological dimension that compared different notions of dimension. No comparison with algebraic dimensions as used in algebraic geometry though, and no fractional dimensions – which I only heard of and don't understand – from fractal geometry either. So what's the dimension of the Cantor set?
Caused by this, Jan-Philipp and me drifted onto the topic of space-filling curves, i.e. curves that completely fill an entire segment of the plane. I remembered that I had taught this at Warwick and that the argument is a rather pretty one: You recursively define a sequence of curves and show that that you'll find a curve to get arbitrarily close to any point in the plane segment. You also show that the curves converge uniformly. Thus the limit exists and is continuous, i.e. a path again, giving you the space filling curve.
Caveats are: You don't get a good way to write that curve explicitly and while you get a bijection from the unit interval to a plane segment, that bijection is not a homeomorphism, i.e. its inverse is not continuous. I could remember all that but I couldn't remember the construction of the curves... Luckily the internet could help out here and, more artistically, here.
Time to go outside now. There's a barbecue, music, cocktails and some of my friends coming as well.
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