Archive for Mathematics

Kloostermania turns 1.0

Since the Pocket Kloostermania has remained unchanged for almost five years, an update is probably welcome! This is now available, in time to honor N. Katz on the occasion of this 71st birthday (which I will help celebrate in China next week). Important changes in the new version: (1) It was recompiled — hence a […]

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Worms, brains and “graphes expanseurs”

Two days ago, I was in Paris and visited the École Polytechnique there (for the first time, as it turns out), in order to give the traditional introductory lecture presenting various aspects of mathematics that is given each year to the incoming class of students. (Many people would wonder how a new class can be […]


Kummer extensions, Hilbert’s Theorem 90 and judicious expansion

This semester, I am teaching “Algebra II” for the first time. After “Algebra I” which covers standard “Groups, rings and fields”, this follow-up is largely Galois theory. In particular, I have to classify cyclic extensions. In the simplest case where is a cyclic extension of degree and contains all -th roots of unity (and is […]

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Noether on Google

Today’s Google doodle celebrates Emmy Noether. Algebra would look very different without her (“successive sets of symbols with the same second suffix“).

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A parity lemma of A. Irving

In his recent work on the divisor function in arithmetic progressions to smooth moduli, A. Irving proves the following rather amusing lemma (see Lemma 4.5 in his paper): Lemma Let be an odd prime number, let be an integer and let be a -tuple of elements of . For any subset of , denote and […]

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