E. Kowalski's blog

Comments on mathematics, mostly.

Jacques Ménard, author of Nicolas Bourbaki

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My punning title about James Maynard must have given me somewhere the undeserved reputation of a Borges specialist, since I’ve just received a curious reworking of the story of Pierre Ménard.

The email address from which it came ( jlb@limbo.ow ) is probably not genuine, so I wonder who the author could be (the final note “Translated, from the Spanish, by H.A.H” is of course suggestive, but one would then like to see the original Spanish…)

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March 4th, 2016 at 7:37 pm

Number Theory Days 2016

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As usual, with Spring comes the annual Number Theory Days of EPFL and ETHZ, this time in Zürich during the week-end of April 15 and 16. The website is online, and the poster should be ready very soon (I will update the post when it is…)

The meeting is organized by the Forschungsinstitut für Mathematik, and (again as usual!) there is a certain amount of funding for local expenses made available by FIM for young researchers (graduate students and postdocs). Please register on the FIM web page before March 21 if you are interested!

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March 3rd, 2016 at 6:16 pm

Posted in ETH,Mathematics

Is MathOverflow insane?

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Since my post contra MathOverflow, already five years ago, I’ve continued watching the site and enjoying many of its mathematical discussions, and seeing myself evolve a bit concerning some of my critical opinions. However, I read today with amazement the discussion that evolved from a question of Richard Stanley on the topic of gravitational waves. I applaud the question, the answer and (among the voices of reason) the comments of Lucia.

The negative comments embody the perfect distillation of the perverse puritanical hair-splitting competition known as “Is this question a good fit for MO?” (to be read in a slightly hysterical voice) that is now what I find most annoying on the site. This is not what mathematics (not even “research” mathematics, that seems to replace here the “pure” mathematics illusion of yesteryears) is about for me. I must confess to finding particularly annoying that some of the most vocal critics (e.g., the pseudonymous “quid”) seem to be people with little actual mathematical contributions and too much time to spend and to write for ever and ever on the finer points of etiquette of a web site as if it were some platonic object to protect from all interlopers.

What would Arnold think of this discussion, where “mathematicians” throw away much (he would say “most”) of the whole history, motivation and insights of their science? Would a question of Kolmogorov on what the brain looks like as graph have passed through the fourches caudines of Signor Quid?

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February 14th, 2016 at 6:40 pm

Posted in Mathematics

New scripts

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I’ve updated my web page on lecture notes with the link to the current version of my script for my probabilistic number theory class (and also with a link to the linear algebra script for the basic year-long linear algebra class for the first-year mathematics and physics students of ETH, although this has little interest beyond the students of the class).

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January 3rd, 2016 at 9:24 pm

Posted in ETH,Mathematics

Probabilistic number theory

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During the fall semester, besides the Linear Algebra course for incoming Mathematics and Physics students, I was teaching a small course on Probabilistic Number Theory, or more precisely on a few aspects of probabilistic number theory that I find especially enjoyable.

Roughly speaking, I concentrated on a small number of examples of statements of convergence in law of sequences of arithmetically-defined probability measures: (1) the Erdös-Kac Theorem; (2) the Bohr-Jessen-Bagchi distribution theorems for the Riemann zeta function on the right of the critical line ; (3) Selberg’s Theorem on the normal behavior of the Riemann zeta function on the critical line ; (4) my own work with W. Sawin on Kloosterman paths. My goal in each case was to do with as little arithmetic, and as much probability, as possible. The reason for this is that I wanted to get and give as clear a picture as possible of which arithmetic facts are involved in each case.

This led to some strange and maybe pedantic-looking discussions at the beginning. But overall I think this was a useful point of view. I think it went especially well in the discussion of Bagchi’s Theorem, which concerns the “functional” limit theorem for vertical translates of the Riemann zeta function in the critical strip, but to the right of the critical line. The proof I gave is, I think, simpler and better motivated than those I have seen (all sources I know follow Bagchi very closely). In the section on Selberg’s Theorem, I used the recent proof found by Radziwill and Soundararajan, which is very elegant (although I didn’t have much time to cover full details during the class).

I have started writing notes for the course, which can be found here. Note that, as usual, the notes are potentially full of mistakes! But those parts which are written are fairly complete, both from the arithmetic and probabilistic point of view.

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January 1st, 2016 at 7:16 pm

Posted in ETH,Mathematics