319 words on Uni
Our usual colloquium-ridden Thursday today. First, Ivan, my office-mate, talked about his work, involving the dangerous – read: not understood by myself – Hochschild-cohomology. Apparently he also knows about orbifolds, so he may be in for a handful of questions shortly...
Later, Günter Ziegler, co-author of Proofs from the Book talked about the Kneser conjecture and how topology and combinatorics are linked. The original proof of the conjecture uses the Borsuk-Ulam theomem – a fascinating theorem stating that any continuous map from an n-dimensional sphere to n-dimensional euclidian space must map two antipodal points, i.e. points opposite on the sphere, to the same point in the euclidian space.
To picture this, just consider the two-dimensional case: Imagine the two dimensional sphere is the surface of the earth and the two-dimensional space is considered pairs of numbers. Now define a map that takes a point on the earth's surface and assigns to it the temperature and the air pressure at that point, i.e. a pair of numbers. Usually you'd assume that temperature and air pressure don't change abruptly but rather continuously as you change the point on the earth's surface. Then the theorem tells you that there must be two opposite points on the earth's surface that have identical temperature and air pressure.
Prof. Kneser was also present. He's quite old now and probably happy that people not only proved the conjecture he made in the sixties about a decade or two later but are still finding nicer proofs and thinking about it in general.
I am supposed to go to Yassin's degree barbecue now but some rain and thunderstorm just started, hm... Amusing cartoon over at The Joy of Tech. That has been done for real in fact by the Chaos Computer Club in Berlin with Pong and more elaborately in Paris last year. There've been similar projects around the world as well, according to their links.
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