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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 <x,y> 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 | <x,y> = 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
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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.
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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!
Aug
22
comment Non-hyperelliptic families of curves with trivial Ceresa class (or Gross-Schoen class)
Wait so I'm completely unaware that it's "generally believed" that non-hyperelliptic curves have non-torsion Ceresa cycle -- who believes this, have they written down why they believe it, etc.?
Aug
21
comment Non-hyperelliptic families of curves with trivial Ceresa class (or Gross-Schoen class)
I just mean etale cohomology -- I suppose this is "really" a motivic question but I don't think I need to invoke anything of that kind to get at what I'm interested in.
Aug
21
asked Non-hyperelliptic families of curves with trivial Ceresa class (or Gross-Schoen class)
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revised Constructing quintic number fields with certain splitting behaviour
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