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Category Archives: Mathematics

The discrete spectrum is discrete

No, this post is not an exercise in tautological reasoning: the point is that the word “discrete” is relatively overloaded. In the theory of automorphic forms, “discrete spectrum” (or “spectre discret”) is the same as “cuspidal spectrum”, and refers to those automorphic representations (of a given group over a given global field ) which are […]

More conjugation shenanigans

After I wrote my last post on the condition in a group, I had a sudden doubt concerning the case in which this arose: there we assume that we have a coset such that for all . I claimed that this implies , but really the argument I wrote just means that : for all […]

Normalizers everywhere

In working on a paper, I found myself in the amusing but unusual situation of having a group , a subgroup and an element such that This certainly can happen: the two obvious cases are when , or when is an involution that happens to be in the normalizer of . In fact the general […]

All Hail the distinguished achievement professor!

Mr. Quomodocumque is probably too modest to mention it himself, so let me be the first mathematics blogger to congratulate Jordan Ellenberg on becoming a Vilas Distinguished Achievement Professor! Which hopefully comes with a lot of free time to visit Switzerland…

The many ways of affineness

Last Saturday, the OED Word of the Day was affineur. Now, I know very well what an affineur is (my favorite is Jean d’Alos, and I especially like his renowned Tome de Bordeaux, the excellence of which can probably be confirmed by Mr. Quomodocumque), but for a few seconds I had in mind the picture […]