E. Kowalski's blog

         Comments on mathematics, mostly.



Filed under: Exercise,Mathematics,Science @ 19:38

Yesterday my younger son was playing dice; the game involved throwing 6 dices simultaneously, and he threw a complete set 1, 2, 3, 4, 5, 6, twice in a row!

Is that a millenial-style coincidence worth cosmic pronouncements? Actually, not that much: since the dices are indistinguishable, the probability of a single throw of this type is

\frac{6!}{6^6}\simeq  0.015432098765432098765432098765432098765,

so about one and a half percent. And for two, assuming independence, we get a probability

\frac{(6!)^2}{6^{12}}\simeq 0.00023814967230605090687395214144185337601,

or a bit more than one chance in five throusand. This is small, but not extraordinarily so.

(The dices are thrown from a cup, so the independence assumption is quite reliable here.)


Bagchi’s thesis

Filed under: Mathematics @ 20:24

Despite everything, there is something to be said for the internet. Just a few days ago, I wanted to reference the work of Bagchi, who provided the probabilistic interpretation of Voronin’s Universality Theorem for the Riemann zeta function. However, the original was unpublished, and one of the few papers of Bagchi on this topic pointedly indicated that he had removed most probabilistic considerations (why? if it was at the request of a referee, I can only sigh). But fortunately, lo and behold, the original thesis (from 1981) can be found in a very decent scan from the Indian Statistical Institute!


Sharks and Snakes

Filed under: Arts,Switzerland @ 18:53

The Swiss stereotypes do not usually suggest a great sense of humor. But since I’ve been in Zürich, I’ve noticed a certain style of quiet understated humor, in particular in advertising.

Here’s one ad for the most famous vegetarian restaurant in Zürich (probably the best in the world):



Here’s an ad for the Zürich public transportation system; the left-hand man is a right-wing politician, and the right-hand one a socialist (I had to look this up; I’m not really up to date on local politics), and the ad says that fortunately there is a tram stop on average every 300 meters…



Here’s a recent ad to warn against swimming in the wrong places in the river, despite the absence of sharks (Hai means shark in German):




My office in 1870

Filed under: Mathematics,Switzerland @ 20:23

The historical “main” building of ETH was finished 150 years ago, in 1864. Or rather, the first version was finished, since it was altered and extended quite a bit since then (as did the surroundings!). In a recent NZZ article, I saw this picture

ETH 1870

ETH in 1870

of the building as it looked in 1870. The red square indicates where my office is located…


Upcoming books

Filed under: Mathematics @ 10:38

As the summer vacations draw to a close, I’d like to point to two upcoming AMS books which might, hopefully, interest some readers…

(1) My lecture notes on representation theory (expanded) will appear in September, published in the Graduate Studies in Mathematics series; the preview material contains Chapter 1, and a fair bit of Chapter 2; the index is also available, and perusing it will give an idea of the range of topics mentioned.

(2) Henryk Iwaniec has also a new book coming, in October, containing his lectures notes on the Riemann zeta function. I haven’t seen it yet, but he told me that the highlight, in his opinion, is the second part which contains his personal treatment of the Levinson method for finding critical zeros of zeta. This should be quite interesting to read…

Update (August 29): the AMS web site confirms that my book is already available!

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