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 Mar 31 comment Local nontriviality of genus-one curves over extensions of degree dividing $6^n$ I don't think so -- the Weil-Chatelet group of an elliptic curve over Q_p has lots of p-power torsion, I think so choosing C to represent a p-torsion class I don't think you can kill this class by restriction to a prime-to-p extension. But maybe I'm confused! Mar 31 comment Detecting a module for the free group algebra on a finite quotient Unfortunately I don't see a good way to interpret my actual question in terms of a virtual Betti number of any Γ. But the thing you do when you compute the abelianization of the kernel of a map Γ -> G is sort of LIKE what I'm asking: by Fox calculus, you have an exact sequence M' -> M -> M'' in the group algebra of Γ, you tensor everything with Z[G] and you take the cohomology in the middle. (Assuming I have this right.) Mar 26 comment Detecting a module for the free group algebra on a finite quotient Yep, this is the way to phrase it to make it sound like a question about representations of finite groups (which I couldn't do...) Mar 25 revised Detecting a module for the free group algebra on a finite quotient added 596 characters in body Mar 25 comment Detecting a module for the free group algebra on a finite quotient Yes, sorry, this is what I'm saying. I will modify the post to clarify. Mar 25 asked Detecting a module for the free group algebra on a finite quotient Nov 26 awarded Nice Answer Nov 17 comment Probability of two vectors lying in the same orthant This is a nice question! One might even ask: what is the joint distribution of against the Hamming distance between the sign vector of x and the sign vector of y? Your question then asks about Pr(Hamming dist = 0 | = theta) in this distribution. Nov 3 comment What happens to the gonality under a finite morphism of curves C' has a map g to P^1 of degree 2k given by composition. If it has another map h to P^1 of smaller degree, you should be able to show (maybe with some extra assumptions) that (g,h): C' -> P^1 x P^1 is birational onto its image. But the image is curve of bidegree at most (2k,2k) so its geometric genus is on order 4k^2 at most. If the genus of C is massively higher than this, you should get a contradiction. So that's one situation where you might know gon(C') = 2k. Oct 29 comment Subsets of [1..N] with no three-term arithmetic progressions and no large gaps Exactly what I needed -- thanks! Oct 29 accepted Subsets of [1..N] with no three-term arithmetic progressions and no large gaps Oct 29 asked Subsets of [1..N] with no three-term arithmetic progressions and no large gaps Oct 17 awarded Popular Question Oct 16 awarded Yearling Jan 7 comment Are there any serious investigations of whether “mathematicians do their best work when they're young”? I haven't read this in years. I have to say, I have learned a lot since then about how to construct a magazine article; this one is kind of confusing, especially where it suddenly veers from general math sociology into a discussion of algebraic topology with no transition. Still, since I am 11 years older now than I was when I wrote that, I heartily endorse its conclusions. Jan 5 awarded Nice Answer Oct 16 awarded Yearling Sep 2 awarded Popular Question Sep 2 awarded Nice Question Aug 26 comment Non-hyperelliptic families of curves with trivial Ceresa class (or Gross-Schoen class) My student Lalit Jain pointed out to me the paper "The Griffiths Infinitesimal Invariant for a Curve in its Jacobian," by Collino and Pirola, which shows that a family of genus-g curves whose codimension in M_g is less than ~g/3 has nontrivial Ceresa. So that's something!